Limiting behavior of inertial manifolds for stochastic differential equations driven by non-Gaussian Levy noise

Abstract: In this paper, we study the limiting behavior for stochastic differential equations driven by non-Gaussian alpha-stable Levy noise as alpha approaches 2. We first prove the convergence of solutions for system driven by alpha-stable Levy noise to those of the system driven by Brownian motion. Then we construct the C^1 inertial manifolds for both systems and show that these inertial manifolds converge in probability as alpha rightarrow2.