On the mild Itô formula in Banach spaces

Abstract

The mild Ito formula proposed in Theorem 1 in [Da Prato, G., Jentzen, A., \& Röckner, M., A mild Ito formula for SPDEs, arXiv:1009.3526 (2012), To appear in the Trans.\ Amer.\ Math.\ Soc.] has turned out to be a useful instrument to study solutions and numerical approximations of stochastic partial differential equations (SPDEs) which are formulated as stochastic evolution equations (SEEs) on Hilbert spaces. In this article we generalize this mild Itô formula so that it is applicable to solutions and numerical approximations of SPDEs which are formulated as SEEs on UMD (unconditional martingale differences) Banach spaces. This generalization is especially useful for proving essentially sharp weak convergence rates for numerical approximations of SPDEs.

27 pages

References in corpus (2)

• Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients
• Exponential moments for numerical approximations of stochastic partial differential equations

Cited by in corpus (2)

• Solving the Kolmogorov PDE by means of deep learning
• Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient