Rough path properties for local time of symmetric α stable process

Qingfeng Wang, Huaizhong Zhao

Research output: Journal PublicationArticlepeer-review

Abstract

In this paper, we first prove that the local time associated with symmetric α-stable processes is of bounded p-variation for any p>[Formula presented] partly based on Barlow's estimation of the modulus of the local time of such processes. The fact that the local time is of bounded p-variation for any p>[Formula presented] enables us to define the integral of the local time ∫−∞α−1f(x)dxLtx as a Young integral for less smooth functions being of bounded q-variation with 1≤q<[Formula presented]. When q≥[Formula presented], Young's integration theory is no longer applicable. However, rough path theory is useful in this case. The main purpose of this paper is to establish a rough path theory for the integration with respect to the local times of symmetric α-stable processes for [Formula presented]≤q<4.

Original languageEnglish
Pages (from-to)3596-3642
Number of pages47
JournalStochastic Processes and their Applications
Volume127
Issue number11
DOIs
Publication statusPublished - Nov 2017

Keywords

  • Itô's formula
  • Local time
  • Rough path
  • Young integral
  • p-variation
  • α-stable processes

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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