Local time penalizations with various clocks for one-dimensional diffusions
Probability
2018-02-19 v2
Abstract
We study some limit theorems for the law of a generalized one-dimensional diffusion weighted and normalized by a non-negative function of the local time evaluated at a parametrized family of random times (which we will call a clock). As the clock tends to infinity, we show that the initial process converges towards a new penalized process, which generally depends on the chosen clock. However, unlike with deterministic clocks, no specific assumptions are needed on the resolvent of the diffusion. We then give a path interpretation of these penalized processes via some universal -finite measures.
Cite
@article{arxiv.1608.07006,
title = {Local time penalizations with various clocks for one-dimensional diffusions},
author = {Christophe Profeta and Kouji Yano and Yuko Yano},
journal= {arXiv preprint arXiv:1608.07006},
year = {2018}
}