Excursions of diffusion processes and continued fractions
Probability
2010-02-11 v2 Mathematical Physics
math.MP
Abstract
It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in terms of an infinite continued fraction. We examine the probabilistic significance of the expansion. To illustrate our results, we discuss some examples of diffusions in deterministic and in random environments.
Cite
@article{arxiv.0906.4651,
title = {Excursions of diffusion processes and continued fractions},
author = {Alain Comtet and Yves Tourigny},
journal= {arXiv preprint arXiv:0906.4651},
year = {2010}
}
Comments
28 pages. Minor changes to Section 5