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The central limit theorem for slow-fast systems with Lévy noise

Xiaoyu Yang, Yong Xu, Ruifang Wang, Zhe Jiao

Abstract

We consider a slow-fast stochastic differential system with Lévy noise. We will employ the perturbed test function method to study the normal deviation of the slow-fast system. Our main result states that the deviation can be approximated by a Gaussian process and the central limit theorem is obtained for the system.

The central limit theorem for slow-fast systems with Lévy noise

Abstract

We consider a slow-fast stochastic differential system with Lévy noise. We will employ the perturbed test function method to study the normal deviation of the slow-fast system. Our main result states that the deviation can be approximated by a Gaussian process and the central limit theorem is obtained for the system.

Paper Structure

This paper contains 3 sections, 1 theorem, 32 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The Main Result

Key Result

Theorem 3.1

Let assumptions (A1) to (A4) hold. Then the normal deviation $\Delta^{\varepsilon}(t)$ converges to $u \left( t \right)$ in the sense of distribution as $\varepsilon$ goes to zero.

Theorems & Definitions (1)

  • Theorem 3.1