Weak averaging principle for multiscale stochastic dynamical systems driven by stable processes

We study the averaging principle for a family of multiscale stochastic dynamical systems. The fast and slow components of the systems are driven by two independent stable Levy noises, whose stable indexes may be different. The homogenizing index r0 of slow components has a relation with the stable index alpha 1 of the noise of fast components given by 0 < r(0 )< 2 - 2/alpha(1). By first studying a nonlocal Poisson equation and then constructing suitable correctors, we obtain that the slow components weakly converge to a Levy process as the scale parameter goes to zero.(c) 2023 Elsevier Inc. All rights reserved.