A Kolmogorov type theorem for stochastic fields

TL;DR

This paper extends the Kolmogorov continuity theorem to stochastic fields with parameters and applies it to establish the continuity of solutions for nonlocal stochastic parabolic equations driven by non-Gaussian Lévy noises.

Contribution

It generalizes the Kolmogorov theorem to a broader class of stochastic fields and applies this to nonlocal stochastic PDEs with Lévy noise.

Findings

Proved a generalized Kolmogorov continuity theorem for stochastic fields.

Established continuity of solutions for nonlocal stochastic parabolic equations.

Extended applicability to non-Gaussian Lévy noise-driven equations.

Abstract

We generalize the Kolmogorov continuity theorem and prove the continuity of a class of stochastic fields with the parameter. As an application, we derive the continuity of solutions for nonlocal stochastic parabolic equations driven by non-Gaussian L\'{e}vy noises.