Large deviation estimates of the crossing probability for pinned Gaussian processes

Details Large deviation estimates of the crossing probability for pinned Gaussian processes Large deviation estimates of the crossing probability for pinned Gaussian processes

2007-02-20

arxiv.org/abs/math/0702573v1

Mathematics

Probability

33 pages. Keywords: conditioned Gaussian processes; reproducing kernel Hilbert spaces; large deviations; exit time probabiliti

Scientific paper

The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in $n$ fixed points at $n$ fixed past instants. In particular, functional large deviation results are stated for small time. Several examples are considered: integrated or not fractional Brownian motion, $m$-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.

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