Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60F10 Large deviations
- 60J60 Diffusion processes [See also 58J65]
- 60G15 Gaussian processes
- 65C50 Other computational problems in probability

**Résumé:** We study a family of importance sampling estimators for the
problem of computing the probability of level crossing when the
crossing level is large, or when the intensity of the noise is
small. We give general results concerning centered gaussian
processes with drift and develop a method which allows to compute
explicitly the asymptotics of the second order moment, with a
special mention for the fractional Brownian Motion case. The main
tools are some refined versions of classical large deviations
results and, for the fractional Brownian Motion, recent results on
changes of probability by Norros et al.

**Mots Clés:** *Importance sampling ; large deviations ; ruin probabilities; Gaussian processes ; fractional
Brownian motion*

**Date:** 2004-01-15

**Prépublication numéro:** *PMA-875*