A Kolmogorov-type theorem for stochastic fields

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 Lévy noises.

Keywords:

• Kolmogorov continuity theorem
• nonlocal stochastic parabolic equations

AMS SUBJECT CLASSIFICATION:

• 60G17
• 60H15

Acknowledgment

The authors are grateful to the referee and the editor for valuable comments and suggestions.

Additional information

Funding

This work was supported in part by National Natural Science Foundation of China grants 11501577, 11771123.