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Large deviation estimates of the crossing probability for pinned Gaussian processes

Part of: Limit theorems Probabilistic methods, simulation and stochastic differential equations Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Lucia Caramellino  and
Barbara Pacchiarotti
Lucia Caramellino*
Affiliation:
Università di Roma Tor Vergata
Barbara Pacchiarotti*
Affiliation:
Università di Roma Tor Vergata
*
∗ Postal address: Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, I-00133 Roma, Italy.
∗ Postal address: Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, I-00133 Roma, Italy.
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Abstract

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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 motions and 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 of the unpinned process.

Keywords

Conditioned Gaussian processreproducing kernel Hilbert spaceslarge deviationsexit time probabilityMonte Carlo method

MSC classification

Primary: 60F10: Large deviations 60G15: Gaussian processes
Secondary: 65C05: Monte Carlo methods

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 2 , June 2008 , pp. 424 - 453
Copyright
Copyright © Applied Probability Trust 2008 

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