Strongly self-interacting processes on the circle
Probability
2019-02-04 v3
Abstract
The purpose of this paper is to investigate the long time behaviour for a self-interacting diffusion and a self-interacting velocity jump process. While the diffusion case has already been studied for some particular potential function, the second one, which belongs to the family of piecewise deterministic processes, is new. Depending on the underlying potential function's shape, we prove either the almost sure convergence or the recurrence for a natural extended process given by a change a variable.
Cite
@article{arxiv.1606.02989,
title = {Strongly self-interacting processes on the circle},
author = {Carl-Erik Gauthier and Pierre Monmarché},
journal= {arXiv preprint arXiv:1606.02989},
year = {2019}
}
Comments
22 pages and 1 figure. Proof of Proposition 2 and proof of the first part of Theorem 1 (Section 5) have been updated. Correction of some typos