Non-local Poisson Equation with Application to Averaging Principle of SDEs with Jumps

Abstract

We study the non-local Poisson equation with a parameter and in the whole space $\mathbb {R}^{d_1}$. Regularities of the solution are obtained under mild assumptions on the coefficients. The result is then used to study the asymptotic behavior of the solution of a singularly perturbed non-local partial differential equation. As an application, we obtain the averaging principle for a fast-slow stochastic dynamical system with Hölder continuous coefficients and driven by multiplicative jump noise. Furthermore, the rate of convergence is also obtained.

Keywords

Non-local Poisson equation / $\alpha $-stable process / Averaging principle / 60H10 / 60J60

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Funding

National Natural Science Foundation of China(11901154)

Rights & permissions

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature