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Local Time Rough Path for Lévy Processes


 
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1. Title Title of document Local Time Rough Path for Lévy Processes
 
2. Creator Author's name, affiliation, country Chunrong Feng; Shanghai Jiaotong University; China
 
2. Creator Author's name, affiliation, country Huaizhong Zhao; Loughborough University; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) semimartingale local time; geometric rough path; Young integral; rough path integral; L'evy processes
 
3. Subject Subject classification 60H05, 58J99
 
4. Description 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 ($1\leq q <3$), we establish the integral $\int _{-\infty}^{\infty}g(x)dL_t^x$ as a Young integral when $1\leq q<2$ and a Lyons' rough path integral when $2\leq q<3$. We therefore apply these path integrals to extend the Tanaka-Meyer formula for a continuous function $f$ if $f^\prime_{-}$ exists and is of finite $q$-variation when $1\leq q<3$, for both continuous semi-martingales and a class of Lévy processes.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 2010-04-29
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/770
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-770
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
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