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 C1 inertial manifolds for both systems and show that these inertial manifolds converge in probability as alpha rightarrow2.
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