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 Electronic Journal of Probability > Vol. 15(2010) > Paper 16 open journal systems 


Local Time Rough Path for Lévy Processes

Chunrong Feng, Shanghai Jiaotong University
Huaizhong Zhao, Loughborough University


Abstract
In this paper, we will prove that the local time of a Lévy process is a rough path of roughness $p$ a.s. for any 2<p<3 under some condition for the Lévy measure. This is a new class of rough path processes. Then for any function g of finite q-variation (1≤ q <3), we establish the integral
∫-∞∞g(x)dLtx as a Young integral when 1≤ q<2 and a Lyons' rough path integral when 2≤ q<3. We therefore apply these path integrals to extend the Tanaka-Meyer formula for a continuous function f if f'- exists and is of finite q-variation when 1≤ q<3 , for both continuous semi-martingales and a class of Lévy processes.


Full text: PDF

Pages: 452-483

Published on: April 29, 2010
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Electronic Journal of Probability. ISSN: 1083-6489