ASYMPTOTIC DISTRIBUTION OF EXIT TIMES FOR SMALL-NOISE DIFFUSIONS

摘要

The asymptotic evaluation of the distribution function F-epsilon Of an exit time is studied for a diffusion process in R(d) with infinitesimal variance O(epsilon). In a generic situation, the dominant term for F-epsilon is derived via the small time approximation of a diffusion process by a Brownian motion. Results improve the logarithmic estimates provided by the large deviations theory. The general analysis is applied to an Ornstein-Uhlenbeck process in R(d). The corresponding function F-epsilon for d = 1 can be used, in particular, to study the grade of service offered to variable bit rate sources in a telecommunication system. [References: 18]