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Representations of Pauli-Fierz type models by path measures. (English) Zbl 07925345

Machihara, Shuji (ed.), Mathematical physics and its interactions. In honor of the 60th birthday of Tohru Ozawa, Tokyo, Japan, August 25–27, 2021. Conference proceedings. Singapore: Springer. Springer Proc. Math. Stat. 451, 283-410 (2024).

MSC: 35-XX

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Zhang, Shuxiong

Upper deviation probabilities for the range of a supercritical super-Brownian motion. (English) Zbl 07923903

Electron. Commun. Probab. 29, Paper No. 42, 8 p. (2024).

MSC: 60J68 60F10 60G57

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Urban, Roman

Feynman formulas for \(qp\)- and \(pq\)-quantization of some Vladimirov type time-dependent Hamiltonians on finite adeles. (English) Zbl 07920845

Anal. Math. Phys. 14, No. 5, Paper No. 105, 38 p. (2024).

MSC: 81S40 81S99 35S05 47D08 11R56

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Hao, Liyao; Tian, Wenyi

Analysis of a WSGD scheme for backward fractional Feynman-Kac equation with nonsmooth data. (English) Zbl 07914908

Adv. Comput. Math. 50, No. 4, Paper No. 87, 26 p. (2024).

MSC: 65M60 65M06 65N30 65M15 26A33 35R11 35R05

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Wang, D.; den Hollander, F.

The annealed parabolic Anderson model on a regular tree. (English) Zbl 07912843

Markov Process. Relat. Fields 30, No. 1, 105-147 (2024).

MSC: 60H15 60H25 05C80 82B44

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Hu, Ying; Wen, Jiaqiang; Xiong, Jie

Backward doubly stochastic differential equations and SPDEs with quadratic growth. (English) Zbl 07904808

Stochastic Processes Appl. 175, Article ID 104405, 22 p. (2024).

MSC: 60H10 60H15 60H30

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Zhang, Lijuan; Wang, Yejuan; Hu, Yaozhong

Feynman-Kac formula for general diffusion equations driven by TFBM with Hurst index \(H \in (0,1)\). (English) Zbl 07901388

J. Differ. Equations 405, 287-336 (2024).

MSC: 60H15 35K05 35R60 60G22

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Meng, Qingyan; Wang, Yejuan; Kloeden, Peter E.; Han, Xiaoying

Existence and uniqueness of solutions for forward and backward nonlocal Fokker-Planck equations with time-dependent coefficients. (English) Zbl 1543.35242

J. Differ. Equations 403, 1-28 (2024).

Reviewer: Alain Brillard (Riedisheim)

MSC: 35Q84 35A01 35A02 60G51 60H30 65C05 35B65 35A24 35R60

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Baraniewicz, Miłosz; Kaleta, Kamil

Integral kernels of Schrödinger semigroups with nonnegative locally bounded potentials. (English) Zbl 07856584

Stud. Math. 275, No. 2, 147-173 (2024).

MSC: 47D08 60J65 35K08

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Wen, Hao; Huang, Jianhua; Zhang, Liang

Stochastic travelling wave of three-species competitive-cooperative systems with multiplicative noise. (English) Zbl 1540.35480

Dyn. Syst. 39, No. 2, 317-343 (2024).

MSC: 35R60 35C07 35K57 60H15

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Sandrić, Nikola

Periodic homogenization of a class of weakly coupled systems of linear PDEs. (English) Zbl 07830975

Comput. Appl. Math. 43, No. 1, Paper No. 57, 26 p. (2024).

MSC: 35B27 35J57 35K45 60F17 60J25 60J60

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Billaud-Friess, Marie; Macherey, Arthur; Nouy, Anthony; Prieur, Clémentine

A probabilistic reduced basis method for parameter-dependent problems. (English) Zbl 1542.65185

Adv. Comput. Math. 50, No. 2, Paper No. 19, 26 p. (2024).

MSC: 65N75 65D15 65N99 68W20 60J65 65C05

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Hu, Yaozhong; Kouritzin, Michael A.; Zheng, Jiayu

Nonlinear McKean-Vlasov diffusions under the weak Hörmander condition with quantile-dependent coefficients. (English) Zbl 07815299

Potential Anal. 60, No. 3, 1093-1119 (2024).

MSC: 60H10 60H30 60H07

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Chen, Yu-Ting

Delta-Bose gas from the viewpoint of the two-dimensional stochastic heat equation. (English) Zbl 1533.60130

Ann. Probab. 52, No. 1, 127-187 (2024).

MSC: 60J55 60J65 60H30

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Junker, Georg

On the path integral formulation of Wigner-Dunkl quantum mechanics. (English) Zbl 1541.81094

J. Phys. A, Math. Theor. 57, No. 7, Article ID 075201, 18 p. (2024).

MSC: 81S40 37A50 31B05

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Zhang, Lijuan; Wang, Yejuan

Feynman-Kac formula for tempered fractional general diffusion equations with nonautonomous external potential. (English) Zbl 1532.60228

Discrete Contin. Dyn. Syst., Ser. B 29, No. 4, 1670-1694 (2024).

MSC: 60K50 35R11 60H30 60G51 26A33

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Lei, Qian; Pun, Chi Seng

Nonlocality, nonlinearity, and time inconsistency in stochastic differential games. (English) Zbl 1536.91042

Math. Finance 34, No. 1, 190-256 (2024).

Reviewer: Alex V. Kolnogorov (Novgorod)

MSC: 91A15

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Pirogov, Sergey; Zhizhina, Elena

Persistence in perturbed contact models in continuum. (English) Zbl 1541.92071

Markov Process. Relat. Fields 29, No. 4, 533-548 (2023).

MSC: 92D25 82C21 82C22 60K35 60J85

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Wen, Hao; Luo, Yantao; Huang, Jianhua; Li, Yuhong

Stochastic travelling wave solution of the \(N\)-species cooperative systems with multiplicative noise. (English) Zbl 1533.92184

Electron. Res. Arch. 31, No. 8, 4406-4426 (2023).

MSC: 92D25 35C07 35K57 60H15

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Cheng, Li-Juan; Thalmaier, Anton

Dimension-free Harnack inequalities for conjugate heat equations and their applications to geometric flows. (English) Zbl 1530.35118

Anal. PDE 16, No. 7, 1589-1620 (2023).

MSC: 35K08 35A08 46E35 42B35 58J35

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Boldt, Sebastian; Güneysu, Batu

Feynman-Kac formula for perturbations of order \(\leq 1\), and noncommutative geometry. (English) Zbl 1527.58009

Stoch. Partial Differ. Equ., Anal. Comput. 11, No. 4, 1519-1552 (2023).

MSC: 58J65 47D03 58J05

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Yang, Minglei; Zhang, Guannan; Del-Castillo-Negrete, Diego; Cao, Yanzhao

A probabilistic scheme for semilinear nonlocal diffusion equations with volume constraints. (English) Zbl 07770183

SIAM J. Numer. Anal. 61, No. 6, 2718-2743 (2023).

MSC: 68Q25 65M75 60J60 65C30

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Kim, Hyun-Jung; Scorolli, Ramiro

A Feynman-Kac approach for the spatial derivative of the solution to the Wick stochastic heat equation driven by time homogeneous white noise. (English) Zbl 1522.60051

Infin. Dimens. Anal. Quantum Probab. Relat. Top. 26, No. 3, Article ID 2350001, 35 p. (2023).

MSC: 60H10 60H30 60H40 60H05

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Urban, R.

Matrix-valued Schrödinger operators over finite adeles. (English) Zbl 1534.81048

Infin. Dimens. Anal. Quantum Probab. Relat. Top. 26, No. 3, Article ID 2250031, 21 p. (2023).

MSC: 81Q05 46S10 11R56 43A25 60J65 70H05 47D08 37M10

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Mazzucchi, Sonia; Moretti, Valter; Remizov, Ivan; Smolyanov, Oleg

Chernoff approximations of Feller semigroups in Riemannian manifolds. (English) Zbl 1529.58014

Math. Nachr. 296, No. 3, 1244-1284 (2023).

Reviewer: Feng-Yu Wang (Tianjin)

MSC: 58J65 58A05 35K15

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Ferré, Grégoire

Stochastic viscosity approximations of Hamilton-Jacobi equations and variance reduction. (English) Zbl 1523.35124

ESAIM, Math. Model. Numer. Anal. 57, No. 4, 2301-2318 (2023).

MSC: 35F21 35R60 60H30 65C05

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Di Persio, Luca; Garbelli, Matteo; Zălinescu, Adrian

Feynman-Kac formula for BSDEs with jumps and time delayed generators associated to path-dependent nonlinear Kolmogorov equations. (English) Zbl 1523.35312

NoDEA, Nonlinear Differ. Equ. Appl. 30, No. 6, Paper No. 72, 36 p. (2023).

MSC: 35R60 60H15 60G51 60H30

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Etoré, P.; León, J. R.; Prieur, C.

A probabilistic point of view for the Kolmogorov hypoelliptic equations. (English) Zbl 1517.60080

ESAIM, Probab. Stat. 27, 668-693 (2023).

MSC: 60H30 60H10 60J35

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Orlov, Yu. N.; Sakbaev, V. Zh.; Shmidt, E. V.

Compositions of random processes in a Hilbert space and its limit distribution. (English) Zbl 1530.81011

Lobachevskii J. Math. 44, No. 4, 1432-1447 (2023).

MSC: 81P05 47B80 60K35 60F05 60J25 47B06 46T12 70M20 46C05 81Q30

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Kuzgun, Sefika; Nualart, David

Feynman-Kac formula for iterated derivatives of the parabolic Anderson model. (English) Zbl 1540.60103

Potential Anal. 59, No. 2, 651-673 (2023).

MSC: 60H07 60H15

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Luo, Tao; Song, Qingshuo

From mean field games to Navier-Stokes equations. (English) Zbl 1520.91051

Numer. Algebra Control Optim. 13, No. 3-4, 486-499 (2023).

MSC: 91A16 35Q30 35Q89 35F21

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Shi, Yufeng; Wen, Jiaqiang; Xiong, Jie

Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs. (English) Zbl 1525.60077

Stochastics 95, No. 3, 396-422 (2023).

MSC: 60H10 60H30

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Sun, Yabing; Zhao, Weidong

Numerical schemes for fully coupled mean-field forward backward stochastic differential equations. (English) Zbl 1515.60252

Discrete Contin. Dyn. Syst., Ser. S 16, No. 5, 999-1013 (2023).

MSC: 60H35 65C05 65C30

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Kopytko, B. I.; Portenko, M. I.

On a multidimensional Brownian motion with a membrane located on a given hyperplane. (English) Zbl 1511.60117

Stochastic Processes Appl. 160, 371-385 (2023).

MSC: 60J65 60J60

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Nagai, Hideo

Optimal consumption-investment under partial information in conditionally log-Gaussian models. (English) Zbl 1509.91039

Probab. Uncertain. Quant. Risk 8, No. 1, 95-120 (2023).

MSC: 91G10 35Q91 49L20 60H30 93E20

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Archer, Eleanor; Pein, Anne

Parabolic Anderson model on critical Galton-Watson trees in a Pareto environment. (English) Zbl 1519.60105

Stochastic Processes Appl. 159, 34-100 (2023).

Reviewer: Isamu Dôku (Saitama)

MSC: 60J80 35K40 60J27

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Baggenstos, Jonas; Salimova, Diyora

Approximation properties of residual neural networks for Kolmogorov PDEs. (English) Zbl 1518.65018

Discrete Contin. Dyn. Syst., Ser. B 28, No. 5, 3193-3215 (2023).

MSC: 65C99 65M75 68T07

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Cho, Junhyun; Yang, Donghee; Kim, Yejin; Lee, Sungchul

An operator splitting method for multi-asset options with the Feynman-Kac formula. (English) Zbl 1538.91097

Comput. Math. Appl. 135, 93-101 (2023).

MSC: 91G60 65M06 65M70 91G20 35R11

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Kutsenko, Vladimir; Yarovaya, Elena

Symmetric branching random walks in random media: comparing theoretical and numerical results. (English) Zbl 1506.60095

Stoch. Models 39, No. 1, 60-79 (2023).

MSC: 60J80 60K37

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Ding, Cuiyang; Zhou, Yijing; Cai, Wei; Zeng, Xuan; Yan, Changhao

A path integral Monte Carlo (PIMC) method based on Feynman-Kac formula for electrical impedance tomography. (English) Zbl 07652777

J. Comput. Phys. 476, Article ID 111862, 19 p. (2023).

MSC: 35Rxx 60Jxx 35Jxx

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Lyu, Yangyang; Li, Heyu

Almost surely time-space intermittency for the parabolic Anderson model with a log-correlated Gaussian field. (English) Zbl 1524.60146

Acta Math. Sci., Ser. B, Engl. Ed. 43, No. 2, 608-639 (2023).

MSC: 60H15 60F99 60G60

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Trusov, N. V.; Shananin, A. A.

Mathematical modeling of the consumer loan market in Russia under sanctions. (English. Russian original) Zbl 1514.91195

Dokl. Math. 106, No. 3, 467-474 (2022); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 507, 71-80 (2022).

MSC: 91G30 91G40 60H30 35Q91

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Urban, Roman

On a diffusion on finite adeles and the Feynman-Kac integral. (English) Zbl 1514.47069

J. Math. Phys. 63, No. 12, Article ID 122101, 18 p. (2022).

MSC: 47D08 60J65 60J70

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Betz, Volker; Polzer, Steffen

A functional central limit theorem for Polaron path measures. (English) Zbl 1509.60090

Commun. Pure Appl. Math. 75, No. 11, 2345-2392 (2022).

MSC: 60F17 60G55 60K05 81S40

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Léonard, Christian

Feynman-Kac formula under a finite entropy condition. (English) Zbl 1502.35060

Probab. Theory Relat. Fields 184, No. 3-4, 1029-1091 (2022).

MSC: 35K20 60H30 60J60

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Forien, Raphaël; Pang, Guodong; Pardoux, Étienne

Multi-patch multi-group epidemic model with varying infectivity. (English) Zbl 1505.92193

Probab. Uncertain. Quant. Risk 7, No. 4, 333-364 (2022).

MSC: 92D30 60H30

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Chen, Zengjing; Liu, Shuhui; Qian, Zhongmin; Xu, Xingcheng

Explicit solutions for a class of nonlinear BSDEs and their nodal sets. (English) Zbl 1502.60089

Probab. Uncertain. Quant. Risk 7, No. 4, 283-300 (2022).

MSC: 60H10 91G80 93E20

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Ding, Cuiyang; Yan, Changhao; Zeng, Xuan; Cai, Wei

A parallel iterative probabilistic method for mixed problems of Laplace equations with the Feynman-Kac formula of killed Brownian motions. (English) Zbl 1501.65003

SIAM J. Sci. Comput. 44, No. 5, A3413-A3435 (2022).

MSC: 65C05 65C30 65N99 92C45

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Bressloff, Paul C.

Diffusion-mediated absorption by partially-reactive targets: Brownian functionals and generalized propagators. (English) Zbl 1506.60085

J. Phys. A, Math. Theor. 55, No. 20, Article ID 205001, 28 p. (2022).

MSC: 60J70

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Bechtold, Florian

Regularization by random translation of potentials for the continuous PAM and related models in arbitrary dimension. (English) Zbl 1501.35466

Electron. Commun. Probab. 27, Paper No. 47, 13 p. (2022).

MSC: 35R60 35K10 60H15 60H50

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Zhou, Quan; Sun, Yabing

High order one-step methods for backward stochastic differential equations via Itô-Taylor expansion. (English) Zbl 1504.65020

Discrete Contin. Dyn. Syst., Ser. B 27, No. 8, 4387-4413 (2022).

MSC: 65C30 60H10 60H35

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Zhang, Wenzhong; Cai, Wei

FBSDE based neural network algorithms for high-dimensional quasilinear parabolic PDEs. (English) Zbl 07599601

J. Comput. Phys. 470, Article ID 111557, 14 p. (2022).

MSC: 60Hxx 65Nxx 35Qxx

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Cygan, Wojciech; Kaleta, Kamil; Śliwiński, Mateusz

Decay of harmonic functions for discrete time Feynman-Kac operators with confining potentials. (English) Zbl 1496.60087

ALEA, Lat. Am. J. Probab. Math. Stat. 19, No. 1, 1071-1101 (2022).

MSC: 60J10 47D08 31C05 60J76 05C81 39A70 35P05 81Q10

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Wen, Hao; Huang, Jianhua; Li, Yuhong

Propagation of stochastic travelling waves of cooperative systems with noise. (English) Zbl 1496.35469

Discrete Contin. Dyn. Syst., Ser. B 27, No. 10, 5779-5803 (2022).

MSC: 35R60 35C07 35K45 35K57 37A25 60H15

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Li, Danping; Liu, Xiaotao; Liu, Hailong

Optimal investment strategy for a family with a random household expenditure under the CEV model. (English) Zbl 07571109

Commun. Stat., Theory Methods 51, No. 17, 5993-6007 (2022).

MSC: 62-XX

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Park, Kevin Min Seong; Stinchcombe, Adam R.

Deep reinforcement learning of viscous incompressible flow. (English) Zbl 07568555

J. Comput. Phys. 467, Article ID 111455, 21 p. (2022).

MSC: 76Dxx 35Qxx 65Mxx

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Milatovic, Ognjen; Saratchandran, Hemanth

Generalized Ornstein-Uhlenbeck semigroups in weighted \(L^p\)-spaces on Riemannian manifolds. (English) Zbl 1509.47067

J. Funct. Anal. 283, No. 8, Article ID 109623, 62 p. (2022).

Reviewer: Mohammed El Aïdi (Bogotá)

MSC: 47D06 47B25 58J05 58J65 35P05 60H30

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Martin, Cameron; Zhang, Hongyuan; Costacurta, Julia; Nica, Mihai; Stinchcombe, Adam R.

Solving elliptic equations with Brownian motion: bias reduction and temporal difference learning. (English) Zbl 1491.65015

Methodol. Comput. Appl. Probab. 24, No. 3, 1603-1626 (2022).

MSC: 65C30 65C05 65N75

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Baker, Graeme; Shkolnikov, Mykhaylo

Zero kinetic undercooling limit in the supercooled Stefan problem. (English. French summary) Zbl 1494.35197

Ann. Inst. Henri Poincaré, Probab. Stat. 58, No. 2, 861-871 (2022).

MSC: 35R35 35K20 60J55 60J70 80A22

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Wang, Hanxiao; Yong, Jiongmin; Zhang, Jianfeng

Path dependent Feynman-Kac formula for forward backward stochastic Volterra integral equations. (English. French summary) Zbl 1494.35071

Ann. Inst. Henri Poincaré, Probab. Stat. 58, No. 2, 603-638 (2022).

MSC: 35D40 35K10 35R60 45D05 60G22 60H20

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Grünbaum, F. Alberto

A Feynman-Kac approach to a paper of Chung and Feller on fluctuations in the coin-tossing game. (English) Zbl 1498.60304

Proc. Am. Math. Soc. 150, No. 9, 4027-4036 (2022).

Reviewer: Romeo Negrea (Timişoara)

MSC: 60J10 60J65 81Q30

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Kopytko, B. I.; Portenko, M. I.

Brownian motion in a Euclidean space with a membrane located on a given hyperplane. (Ukrainian. English summary) Zbl 1499.60276

Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2022, No. 1, 3-10 (2022).

MSC: 60J65 60J60

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Cho, Junhyun; Kim, Yejin; Lee, Sungchul

An accurate and stable numerical method for option hedge parameters. (English) Zbl 1510.91181

Appl. Math. Comput. 430, Article ID 127276, 11 p. (2022).

MSC: 91G60 65M06 91G20

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Huang, Qiao; Duan, Jinqiao; Song, Renming

Homogenization of nonlocal partial differential equations related to stochastic differential equations with Lévy noise. (English) Zbl 1504.60100

Bernoulli 28, No. 3, 1648-1674 (2022).

Reviewer: Maria Gordina (Storrs)

MSC: 60H15 60J60 35B27 60G51

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Platonova, M. V.

An analogue of the Feynman-Kac formula for a high-order operator. (English. Russian original) Zbl 07523559

Theory Probab. Appl. 67, No. 1, 62-76 (2022); translation from Teor. Veroyatn. Primen. 67, No. 1, 81-99 (2022).

Reviewer: Feng-Yu Wang (Tianjin)

MSC: 47D06 47B35 60G57

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Ren, Panpan; Röckner, Michael; Wang, Feng-Yu

Linearization of nonlinear Fokker-Planck equations and applications. (English) Zbl 1486.60104

J. Differ. Equations 322, 1-37 (2022).

MSC: 60J60 58J65 60B05

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Bayer, Christian; Qiu, Jinniao; Yao, Yao

Pricing options under rough volatility with backward SPDEs. (English) Zbl 1484.91469

SIAM J. Financ. Math. 13, No. 1, 179-212 (2022).

MSC: 91G20 60H15 60G40 91G60

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Sun, Shengqiu

Backward stochastic differential equations driven by \(G\)-Brownian motion with uniformly continuous coefficients in \((y, z)\). (English) Zbl 1498.60239

J. Theor. Probab. 35, No. 1, 370-409 (2022).

MSC: 60H10 60H30

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Lyu, Yangyang

Spatial asymptotics for the Feynman-Kac formulas driven by time-dependent and space-fractional rough Gaussian fields with the measure-valued initial data. (English) Zbl 1480.60192

Stochastic Processes Appl. 143, 106-159 (2022).

MSC: 60H30 60F10 60G15 60H40

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Yoshioka, Hidekazu; Yaegashi, Yuta; Tsujimura, Motoh; Yoshioka, Yumi

Cost-efficient monitoring of continuous-time stochastic processes based on discrete observations. (English) Zbl 07887586

Appl. Stoch. Models Bus. Ind. 37, No. 1, 113-138 (2021).

MSC: 62-XX

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Liu, Fei

On a tilted Liouville-master equation of open quantum systems. (English) Zbl 1521.81126

Commun. Theor. Phys. 73, No. 9, Article ID 095601, 7 p. (2021).

MSC: 81S22 47D08 80M60

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Yang, Minglei; Zhang, Guannan; del-Castillo-Negrete, Diego; Stoyanov, Miroslav; Beidler, Matthew

A sparse-grid probabilistic scheme for approximation of the runaway probability of electrons in fusion tokamak simulation. (English) Zbl 1497.60093

Bungartz, Hans-Joachim (ed.) et al., Sparse grids and applications – Munich 2018. Selected papers based on the presentations at the fifth workshop, SGA2018, Munich, Germany, July 23–27, 2018. Cham: Springer. Lect. Notes Comput. Sci. Eng. 144, 245-264 (2021).

MSC: 60H35 65C30 65D40 65M75

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Yang, Minglei; Zhang, Guannan; del-Castillo-Negrete, Diego; Stoyanov, Miroslav

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems. (English) Zbl 07515456

J. Comput. Phys. 444, Article ID 110564, 19 p. (2021).

MSC: 60Jxx 60Hxx 65Cxx

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Kassel, Adrien; Lévy, Thierry

Covariant Symanzik identities. (English) Zbl 1483.60112

Probab. Math. Phys. 2, No. 3, 419-475 (2021).

MSC: 60J55 60J57 81T25 82B20

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Braun, Mathias; Güneysu, Batu

Heat flow regularity, Bismut-Elworthy-Li’s derivative formula, and pathwise couplings on Riemannian manifolds with Kato bounded Ricci curvature. (English) Zbl 07478658

Electron. J. Probab. 26, Paper No. 129, 25 p. (2021).

MSC: 47D08 53C21 58J35 58J65

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González Casanova, Adrián; Kurt, Noemi; Tóbiás, András

Particle systems with coordination. (English) Zbl 1482.60117

ALEA, Lat. Am. J. Probab. Math. Stat. 18, No. 2, 1817-1844 (2021).

MSC: 60J90 60J80 92D15 92D25 60G50

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Matte, Oliver

Feynman-Kac formulas for Dirichlet-Pauli-Fierz operators with singular coefficients. (English) Zbl 1492.47042

Integral Equations Oper. Theory 93, No. 6, Paper No. 62, 54 p. (2021).

MSC: 47D08 60H30 81V10 81V80

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Deligiannidis, G.; Maurer, S.; Tretyakov, M. V.

Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation. (English) Zbl 1493.65019

BIT 61, No. 4, 1223-1269 (2021).

MSC: 65C30 60H10 35R09 60H35 60G50

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Lamarre, Pierre Yves Gaudreau

Semigroups for one-dimensional Schrödinger operators with multiplicative Gaussian noise. (English) Zbl 1494.47080

Electron. J. Probab. 26, Paper No. 107, 47 p. (2021).

MSC: 47D08 47H40 60J55

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Nonsoong, P.; Mekchay, K.; Rujivan, S.

An analytical option pricing formula for mean-reverting asset with time-dependent parameter. (English) Zbl 1471.91582

ANZIAM J. 63, No. 2, 178-202 (2021).

MSC: 91G20 35Q91

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Wang, Feng-Yu

Image-dependent conditional McKean-Vlasov SDEs for measure-valued diffusion processes. (English) Zbl 1470.60227

J. Evol. Equ. 21, No. 2, 2009-2045 (2021).

MSC: 60J60 58J65

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Cavalli, Benedetta

A probabilistic view on the long-time behaviour of growth-fragmentation semigroups with bounded fragmentation rates. (English) Zbl 1470.60209

ESAIM, Probab. Stat. 25, 258-285 (2021).

MSC: 60J25 35Q92 47D06 47G20 60G51

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Beck, Christian; Gonon, Lukas; Hutzenthaler, Martin; Jentzen, Arnulf

On existence and uniqueness properties for solutions of stochastic fixed point equations. (English) Zbl 1462.60096

Discrete Contin. Dyn. Syst., Ser. B 26, No. 9, 4927-4962 (2021).

MSC: 60H30 60H10 45G10 47H10

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Nualart, David; Song, Xiaoming; Zheng, Guangqu

Spatial averages for the parabolic Anderson model driven by rough noise. (English) Zbl 1464.60019

ALEA, Lat. Am. J. Probab. Math. Stat. 18, No. 1, 907-943 (2021).

MSC: 60F05 60H15 60H07 60G15

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Fan, Wai-Tong Louis; Hu, Wenqing; Terlov, Grigory

Wave propagation for reaction-diffusion equations on infinite random trees. (English) Zbl 1462.82024

Commun. Math. Phys. 384, No. 1, 109-163 (2021).

MSC: 82C20 82D99 05C05 05C80 60J65 60J60 60F10 60B20 15B52 35C07 35Q92

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Lin, Lin; Xu, Fang; Zhang, Qi

The link between stochastic differential equations with non-Markovian coefficients and backward stochastic partial differential equations. (English) Zbl 1480.60165

Acta Math. Sin., Engl. Ser. 37, No. 3, 447-457 (2021).

MSC: 60H10 60H15 93E20

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Murayama, Taro

A third representation of Feynman-Kac-Itô formula with singular magnetic vector potential. (English) Zbl 1480.60143

Lett. Math. Phys. 111, No. 2, Paper No. 33, 21 p. (2021); correction ibid. 111, No. 2, Paper No. 49, 1 p. (2021).

MSC: 60H05 60J65 81S40

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Leschke, Hajo; Rothlauf, Sebastian; Ruder, Rainer; Spitzer, Wolfgang

The free energy of a quantum Sherrington-Kirkpatrick spin-glass model for weak disorder. (English) Zbl 1462.82078

J. Stat. Phys. 182, No. 3, Paper No. 55, 42 p. (2021).

MSC: 82D30 82B44 60G15 60F10 60G55 60J20

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Grishin, Denis V.; Pavlovskiy, Yan Yu.

Representation of solutions of the Cauchy problem for a one-dimensional Schrödinger equation with a smooth bounded potential by quasi-Feynman formulae. (English. Russian original) Zbl 1460.81017

Izv. Math. 85, No. 1, 24-60 (2021); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 85, No. 1, 27-65 (2021).

MSC: 81Q05 47D08 35C15 35J10 35L04

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Sandrić, Nikola; Valentić, Ivana

A CLT for degenerate diffusions with periodic coefficients, and application to homogenization of linear PDEs. (English) Zbl 1460.35022

J. Differ. Equations 282, 233-271 (2021).

Reviewer: Adrian Muntean (Karlstad)

MSC: 35B27 35J70 35K65 60F17 60J25

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Wang, Hanxiao

Extended backward stochastic Volterra integral equations, quasilinear parabolic equations, and Feynman-Kac formula. (English) Zbl 1470.60143

Stoch. Dyn. 21, No. 1, Article ID 2150004, 37 p. (2021).

MSC: 60H05 60H20 45D05 35K40 35K59

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Pozza, Marco

Representation formula for viscosity solution to a PDE problem involving Pucci’s extremal operator. (English) Zbl 1454.35049

Nonlinear Anal., Real World Appl. 57, Article ID 103199, 13 p. (2021).

MSC: 35D40 35C15 35J25

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Chen, Mu-Fa; Mao, Yong-Hua

Introduction to stochastic processes. Translated from the Chinese. Originally published under the same title by Higher Education Press, Beijing 2007. (English) Zbl 1471.60001

World Scientific Series on Probability Theory and Its Applications 2. Beijing: Higher Education Press; Hackensack, NJ: World Scientific (ISBN 978-981-4740-30-2/hbk; 978-981-4740-32-6/ebook). xiii, 230 p. (2021).

MSC: 60-01 60G05 60J10 60J27 60J60

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Huang, Zongyuan; Wang, Haiyang; Wu, Zhen; Yu, Zhiyong

Quadratic reflected BSDEs and related obstacle problems for PDEs. (English) Zbl 07549051

Commun. Stat., Theory Methods 49, No. 3, 567-589 (2020).

MSC: 60H10 35K10

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Lejay, Antoine; González, Hernán Mardones

A forward-backward probabilistic algorithm for the incompressible Navier-Stokes equations. (English) Zbl 07506618

J. Comput. Phys. 420, Article ID 109689, 19 p. (2020).

MSC: 76-XX 65-XX

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Wang, Bao; Yuan, Binjie; Shi, Zuoqiang; Osher, Stanley J.

EnResNet: ResNets ensemble via the Feynman-Kac formalism for adversarial defense and beyond. (English) Zbl 1508.68312

SIAM J. Math. Data Sci. 2, No. 3, 559-582 (2020).

MSC: 68T07

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Rajeev, B.

On the Feynman-Kac formula. (English) Zbl 1468.60082

Joshua, V. C. (ed.) et al., Applied probability and stochastic processes. Selected papers based on the presentations at the international conference, Kerala, India, January, 7–10 2019. In honour of Prof. Dr. A. Krishnamoorthy. Singapore: Springer. Infosys Sci. Found. Ser., 491-506 (2020).

MSC: 60H15 60H10 60B11