Almost sure asymptotics for a diffusion process in a drifted Brownian potential
Alexis Devulder (PMA)
TL;DR
This paper investigates the asymptotic behavior of a one-dimensional diffusion in a drifted Brownian potential, focusing on hitting times and their upper functions, and establishes an iterated logarithm law for lower limits.
Contribution
It provides a detailed characterization of hitting times' upper functions and lower limits for diffusion in a drifted Brownian potential, advancing understanding of its asymptotic properties.
Findings
Characterized upper functions of hitting times.
Established iterated logarithm law for lower limits.
Provided new insights into diffusion in drifted Brownian potentials.
Abstract
We study a one-dimensional diffusion process in a drifted Brownian potential. We characterize the upper functions of its hitting times in the sense of Paul L\'evy, and determine the lower limits in terms of an iterated logarithm law.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Stochastic processes and financial applications · Markov Chains and Monte Carlo Methods