Strong and weak convergence rates for slow–fast stochastic differential equations driven by α-stable process

Abstract

Multiscale models involving “slow” and “fast” components appear naturally in various fields, such as nonlinear oscillations, chemical kinetics, biology, climate dynamics, etc, see, e.g., [3,12,22,33] and the references therein. The averaging principle of multiscale models describes the asymptotic behavior of the slow components as the scale parameter → 0. In [23], Khasminskii considered a class of multiscale stochastic differential equations (SDEs for short) driven by Wiener noise, i.e.,  dX t = A(X t , Y t )dt+ dWt, X 0 = x ∈ R, dY t = 1 B(X t , Y t )dt+ 1 √ dWt, Y 0 = y ∈ R,