A note on maximal estimates for stochastic convolutions

TL;DR

This paper introduces a new sufficient condition ensuring the pathwise continuity of stochastic convolutions in Banach spaces, which is crucial for understanding regularity in stochastic partial differential equations.

Contribution

It provides a novel criterion for pathwise regularity of stochastic convolutions, advancing the theoretical understanding in stochastic PDE analysis.

Findings

New sufficient condition for pathwise continuity

Applicable to Banach space-valued stochastic convolutions

Enhances regularity analysis in stochastic PDEs

Abstract

In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.