The Maximum of the Local Time of a Diffusion Process in a Drifted Brownian Potential
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- 刊名：Lecture Notes in Mathematics
- 出版年：2016
- 出版时间：2016
- 年：2016
- 卷：2168
- 期：1
- 页码：123-177
- 全文大小：848 KB
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16. Laboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 78035, Versailles, France - 丛书名：Séminaire de Probabilités XLVIII
- ISBN：978-3-319-44465-9
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Probability Theory and Stochastic Processes
Dynamical Systems and Ergodic Theory
Mathematical Biology
Partial Differential Equations
Functional Analysis
Abstract Harmonic Analysis
Group Theory and Generalizations - 出版者：Springer Berlin / Heidelberg
- ISSN：1617-9692
- 卷排序：2168
文摘
We consider a one-dimensional diffusion process X in a (−κ∕2)-drifted Brownian potential for κ ≠ 0. We are interested in the maximum of its local time, and study its almost sure asymptotic behaviour, which is proved to be different from the behaviour of the maximum local time of the transient random walk in random environment. We also obtain the convergence in law of the maximum local time of X under the annealed law after suitable renormalization when κ ≥ 1. Moreover, we characterize all the upper and lower classes for the hitting times of X, in the sense of Paul Lévy, and provide laws of the iterated logarithm for the diffusion X itself. To this aim, we use annealed technics.