2006/04/04 by Alexis Devulder, Devulder, Alexis
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.math/0604078
openalex publication_date 2006/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.