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A mild Itô formula for SPDEs. (English) Zbl 1423.35472

The authors introduce the notion of mild Itô processes and derive the mild Itô-type formula for the such processes. As an examples of mild Itô processes one can considers mild solutions of stochastic partial differential equations and their numerical approximation processes. It is shown how the mild Itô formula can be used to derive improved a priori bounds for stochastic partial differential equations. The mild Itô formula is used to establish improved Hölder continuity properties for solutions of Kolmogorov partial differential equations in Hilbert spaces. Euler-type and Milstein-type approximations for stochastic partial differential equations can be formulated as mild Itô processes. The mild Itô formula is used to solve the weak convergence problem for such-type numerical approximations of stochastic partial differential equations with nonlinear diffusion coefficients.

MSC:

35R60 PDEs with randomness, stochastic partial differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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