| Título: | Local Time Rough Path for Lévy Processes |
| Autores: |
Feng, Chunrong; Shanghai Jiaotong University Zhao, Huaizhong; Loughborough University |
| Fecha: | 2010-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
semimartingale local time; geometric rough path; Young integral; rough path integral; L'evy processes 60H05, 58J99 |
| Descripción: | 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. |
| Idioma: | No aplica |
1 Lévy Classes and Self-Normalization por Khoshnevisan, Davar; University of Utah | 6 Time-Space Analysis of the Cluster-Formation in Interacting Diffusions por Fleischmann, Klaus; Weierstrass Institute for Applied Analysis and Stochastics,Greven, Andreas; Universitat Erlangen-Nurnberg |
2 Hausdorff Dimension of Cut Points for Brownian Motion por Lawler, Gregory F.; Duke University and Cornell University | 7 Conditional Moment Representations for Dependent Random Variables por Bryc, Wlodzimierz; University of Cincinnati |
3 Eigenvalue Expansions for Brownian Motion with an Application to Occupation Times por Bass, Richard F.; University of Washington,Burdzy, Krzysztof; University of Washington | 8 Almost Sure Exponential Stability of Neutral Differential Difference Equations with Damped Stochastic Perturbations por Liao, Xiao Xin; University of Strathclyde,Mao, Xuerong; University of Strathclyde |
4 Random Discrete Distributions Derived from Self-Similar Random Sets por Pitman, Jim; University of California, Berkeley,Yor, Marc; Université Pierre et Marie Curie | 9 Quantitative Bounds for Convergence Rates of Continuous Time Markov Processes por Roberts, Gareth O.; University of Cambridge,Rosenthal, Jeffrey S.; University of Toronto |
5 A Microscopic Model for the Burgers Equation and Longest Increasing Subsequences por Seppäläinen, Timo; Iowa State University | 10 Metastability of the Three Dimensional Ising Model on a Torus at Very Low Temperatures por Ben Arous, Gérard; Ecole Normale Supérieure,Cerf, Raphaël; Université Paris Sud |