Transience, recurrence and speed of diffusions with a non-Markovian two-phase "use it or lose it" drift
Probability
2012-10-10 v1
Abstract
We investigate the transience/recurrence of a non-Markovian, one-dimensional diffusion process which consists of a Brownian motion with a non-anticipating drift that has two phases---a transient to mode which is activated when the diffusion is sufficiently near its running maximum, and a recurrent mode which is activated otherwise. We also consider the speed of a diffusion with a two-phase drift, where the drift is equal to a certain positive constant when the diffusion is sufficiently near its running maximum, and is equal to another positive constant otherwise.
Keywords
Cite
@article{arxiv.1210.2443,
title = {Transience, recurrence and speed of diffusions with a non-Markovian two-phase "use it or lose it" drift},
author = {Ross G. Pinsky},
journal= {arXiv preprint arXiv:1210.2443},
year = {2012}
}