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

TL;DR

This paper investigates how solutions and inertial manifolds of stochastic differential equations driven by non-Gaussian Levy noise behave as the Levy parameter approaches 2, showing convergence to Brownian motion systems.

Contribution

It establishes the convergence of solutions and inertial manifolds for Levy-driven SDEs to those driven by Brownian motion as alpha approaches 2.

Findings

Solutions converge as alpha approaches 2.

Inertial manifolds converge in probability.

Constructed C^1 inertial manifolds for both systems.

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.