• P. BALDI
• B. PACCHIAROTTI

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