Optimal Regularity of Stochastic Evolution Equations in M-type 2 Banach Spaces

Abstract

In this paper, we prove the well-posedness and op- timal trajectory regularity for the solution of stochastic evolution equations driven by general multiplicative noises in martingale type 2 Banach spaces. The main idea of our method is to combine the approach in [HL] dealing with Hilbert setting and a version of Burkholder inequality in M-type 2 Banach space. Applying our main results to the stochastic heat equation gives a positive an- swer to an open problem proposed in [JR12].

17 pages

References in corpus (2)

• Stochastic integration in UMD Banach spaces
• Well-posedness and Optimal Regularity of Stochastic Evolution Equations with Multiplicative Noises

Cited by in corpus (4)

• Strong Approximation of Monotone Stochastic Partial Differential Equations Driven by Multiplicative Noise
• Well-posedness and Optimal Regularity of Stochastic Evolution Equations with Multiplicative Noises
• Harnack Inequalities and Ergodicity of Stochastic Reaction-Diffusion Equation in $L^p$
• Strong convergence of numerical discretizations for semilinear stochastic evolution equations driven by multiplicative white noise