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Small ball probability of collision local time for symmetric stable processes

Minhao Hong, Qian Yu

Abstract

In this article, the small ball probability is obtained for the collision local time of two independent symmetric $α-$stable processes with parameters $α_1,α_2\in(0,2]$ satisfying $\max\{α_1,α_2\}>1$. The proof is based on obtaining the asymptotic behavior of moment generating function by contour integration.

Small ball probability of collision local time for symmetric stable processes

Abstract

In this article, the small ball probability is obtained for the collision local time of two independent symmetric stable processes with parameters satisfying . The proof is based on obtaining the asymptotic behavior of moment generating function by contour integration.
Paper Structure (5 sections, 11 theorems, 104 equations)

This paper contains 5 sections, 11 theorems, 104 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of main theorem
  4. Technical Lemmas
  5. The proof of Proposition \ref{['Tauberian']}

Key Result

Proposition 1.1

Let $Z$ be a non-negative random variable. If $\lim_{\lambda \to \infty} \lambda \mathbb{E}[e^{-\lambda Z}] = C \in (0,\infty)$, then

Theorems & Definitions (22)

  • Remark 1.1
  • Proposition 1.1
  • Proposition 1.2
  • Theorem 1.1
  • Remark 1.2
  • Corollary 1.1
  • Definition 2.1
  • Lemma 2.1
  • proof : The proof of Lemma \ref{['reciprocal']}
  • Lemma 2.2
  • ...and 12 more