Large deviation estimates of the crossing probability for pinned Gaussian processes
Probability
2016-04-06 v1
Abstract
The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in fixed points at fixed past instants. In particular, functional large deviation results are stated for small time. Several examples are considered: integrated or not fractional Brownian motion, -fold integrated Brownian motion. As an application, the asymptotic behavior of the exit probability is studied and used for the practical purpose of the numerical computation, via Monte Carlo methods, of the hitting probability up to a given time.
Cite
@article{arxiv.math/0702573,
title = {Large deviation estimates of the crossing probability for pinned Gaussian processes},
author = {L. Caramellino and B. Pacchiarotti},
journal= {arXiv preprint arXiv:math/0702573},
year = {2016}
}
Comments
33 pages. Keywords: conditioned Gaussian processes; reproducing kernel Hilbert spaces; large deviations; exit time probabilities; Monte Carlo methods