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arXiv · 1709.08472

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

Jialin Hong·Chuying Huang·Zhihui Liu
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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].

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Jialin Hong, Chuying Huang, Zhihui Liu. 2017-09-25. Optimal Regularity of Stochastic Evolution Equations in M-type 2 Banach Spaces. https://doi.org/10.1016/j.jde.2019.03.003

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