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Convergence rate of the Smoluchowski-Kramers approximation for diffusions with jumps

Chungang Shi

Abstract

In the paper, the Kolmogorov distance is used to study the Smoluchowski-Kramers approximation for diffusions with jumps. The convergence rate is derived by Malliavin calculus.

Convergence rate of the Smoluchowski-Kramers approximation for diffusions with jumps

Abstract

In the paper, the Kolmogorov distance is used to study the Smoluchowski-Kramers approximation for diffusions with jumps. The convergence rate is derived by Malliavin calculus.
Paper Structure (3 sections, 8 theorems, 92 equations)

This paper contains 3 sections, 8 theorems, 92 equations.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Main results

Key Result

Proposition 1

If $u$ belongs to $\mathbb{L}_{a}^{1,N}$ then the stochastic integrals belongs to $\mathbb{D}^{1,N}$ and for almost all $(\tau,\alpha)\in\mathbb{R}_{+}\times\mathbb{R}_{0}$,

Theorems & Definitions (13)

  • Proposition 1
  • Lemma 2: A
  • Lemma 3
  • proof
  • Proposition 4
  • proof
  • Proposition 5
  • Lemma 6
  • proof
  • Lemma 7
  • ...and 3 more