A note on sufficient conditions of asymptotic stability in distribution of stochastic differential equations with \(G\)-Brownian motion. (English) Zbl 1499.60186
Summary: This paper investigates a sufficient condition of asymptotic stability in distribution of stochastic differential equations driven by \(G\)-Brownian motion \((G\)-SDEs). We define the concept of asymptotic stability in distribution under sublinear expectations. Sufficient criteria of the asymptotic stability in distribution based on sublinear expectations are given. Finally, an illustrative example is provided.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60G65 | Nonlinear processes (e.g., \(G\)-Brownian motion, \(G\)-Lévy processes) |
| 93E15 | Stochastic stability in control theory |
Keywords:
\(G\)-SDEs; sublinear expectation; stability in distribution; Markovian inequality; \(G\)-Itô formulaReferences:
| [1] | Du, N. H.; Dang, N. H.; Dieu, N. T., On stability in distribution of stochastic differential delay equations with Markovian switching, Systems Control Lett., 65, 43-49 (2014) · Zbl 1285.93102 |
| [2] | Li, X.; Liu, W.; Luo, Q.; Mao, X., Stabilization in distribution of hybrid stochastic differential equations by feedback control based on discrete-time state observations, Aotomatica, 140, Article 110210 pp. (2022) · Zbl 1485.93611 |
| [3] | You, S.; Hu, L.; Lu, J.; Mao, X., Stabilisation in distribution by delay feedback control for hybrid stochastic differential equations, IEEE Trans. Automat. Control (2021) |
| [4] | Peng, S., Nonlinear Expectations and Stochastic Calculus under Uncertainty (2019), Springer: Springer Berlin · Zbl 1427.60004 |
| [5] | Fei, C.; Fei, W.; Mao, X.; Yan, L., Delay-dependent asymptotic stability of highly nonlinear stochastic differential delay equations driven by \(G\)-Brownian motion, J. Franklin Inst. B, 359, 9, 4366-4392 (2022) · Zbl 1491.93100 |
| [6] | Fei, C.; Fei, W.; Yan, L., Existence-uniqueness and stability of solutions to highly nonlinear stochastic differential delay equations driven by \(G\)-Brownian motions, Appl. Math. J. Chinese Univ., 34, 2, 184-204 (2019) · Zbl 1438.60071 |
| [7] | Chen, Z., Strong laws of large numbers for sub-linear expectations, Sci. China Math., 59, 5, 945-954 (2016) · Zbl 1341.60015 |
| [8] | Chen, Z.; Wu, P.; Li, B., A strong law of large numbers for non-additive probabilities, Internat. J. Approx. Reason., 54, 365-377 (2013) · Zbl 1266.60051 |
| [9] | Ikeda, N.; Watanabe, S., Stochastic Differential Equations and Diffusion Processes (1981), North-Holland: North-Holland Amsterdam · Zbl 0495.60005 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
