Uniform large deviations for stochastic Burgers–Huxley equation driven by multiplicative noise

Abstract

In this paper, we establish a Freidlin–Wentzell type large deviation principle uniformly with respect to initial condition in bounded subsets of an infinite dimensional Banach space for stochastic Burgers–Huxley equation driven by multiplicative small noise. The proof is based on the weak convergence approach obtained by Salins, Budhiraja, Dupuis (Trans. Amer. Math. Soc., 2019).

Keywords:

• Large deviations principle
• uniform large deviations principle
• stochastic Burgers–Huxley equation
• weak convergence approach

AMS Subject Classifications:

• Primary 60F10
• Secondary 60H15

Acknowledgments

We would like to thank the referees for their helpful suggestions which allowed us to improve the presentation of our paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partly supported by National Key R&D Program of China (No. 2020YFA0712700), National Natural Science Foundation of China (No. 11931004, 12090014, 11971273), Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (No. 2008DP173182), Beijing Institute of Technology Research Fund Program for Young Scholars.