Stochastic heat equation and martingale differences

ABSTRACT

We prove an approximation in law of the real-valued mild solution for a class of semilinear stochastic heat equation driven by an additive fractional noise using martingale differences under suitable assumptions.

KEYWORDS:

• Fractional noise
• Martingale differences
• Stochastic heat equation
• Weak convergence

MATHEMATICS SUBJECT CLASSIFICATION:

• 60B10
• 60G15
• 60H15

Acknowledgments

The authors are grateful to the anonymous referees and the associate editor for valuable comments and suggestions to improve this paper.

Funding

This work was supported by National Natural Science Foundation-Mathematical Tianyuan Foundation of China [grant number 11526117], Zhejiang Provincial Natural Science Foundation [grant number LQ16A010006] and the Natural Science Foundation of Ningbo Municipality [grant number 2015A610158].