Abstract
Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved.
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Gyöngy, I. and Krylov, N.V.: ‘On stochastic equations with respect to semimartingales II. Ito formula in Banach spaces’, Stochastics 6 (1982), 153–173.
Gyöngy, I.: ‘On stochastic equations with respect to semimartingales III’, Stochastics 7 (1982), 231–254.
Gyöngy, I.: ‘Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise II’, Potential Anal. 11 (1999), 1–37.
Gyöngy, I. and Martinez, T.: ‘Solutions of partial differential equations as extremals of convex functionals’, submitted for publication.
Krylov, N.V.: ‘Extremal properties of solutions of stochastic equations’, Theory Probab. Appl. 29 (1984), 209–221.
Krylov, N.V. and Rosovskii, B.L.: ‘Stochastic evolution equations’, J. Soviet Math. 16 (1981), 1233–1277.
Lions, J.L.: Quelques méthodes de résolution des problèmes aux limites non linéaires, Études mathématiques, Dunod Gauthiers-Villars, 1969.
Pardoux, E.: ‘Équations aux dérivées partielles stochastiques nonlinéares monotones. Étude de solutions fortes de type Itô’, Thése Doct. Sci. Math. Univ. Paris Sud., 1975.
Pardoux, E.: ‘Stochastic partial differential equations and filtering of diffusion processes’, Stochastics 3(2) (1979), 127–167.
Pardoux, E.: ‘Filtrage non linéaire et équations aux derivées partielles stochastiques associées’, École d’été de Probabilités de Saint-Flour, 1989.
Rozovskii, B.: Stochastic Evolution Systems. Linear Theory and Applications to Nonlinear Filtering, Kluwer, Dordrecht.
Zeidler, E.: Nonlinear Functional Analysis and its Applications, Springer-Verlag, New York, 1990.
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Mathematics Subject Classifications (2000)
Primary: 60H15; Secondary: 65M60.
István Gyöngy: This paper was written while the first named author was visiting the University of Paris X. The research of this author is partially supported by EU Network HARP.
Annie Millet: The research of the second named author is partially supported by the research project BMF2003-01345.
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Gyöngy, I., Millet, A. On Discretization Schemes for Stochastic Evolution Equations. Potential Anal 23, 99–134 (2005). https://doi.org/10.1007/s11118-004-5393-6
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DOI: https://doi.org/10.1007/s11118-004-5393-6