ASYMPTOTIC RESULTS FOR EXIT PROBABILITIES OF STOCHASTIC
PROCESSES GOVERNED BY AN INTEGRAL TYPE RATE FUNCTION
Mario Abundo
Claudio Macci
Gabriele Stabile
Abstract: In this paper we present asymptotic results for exit probabilities of stochastic processes
in the fashion of large deviations. The main result concerns stochastic processes which satisfy
the large deviation principle with an integral type rate function. We also present results for
exit probabilities of linear diffusions and particular growth processes, and we give two
examples.
2000 AMS Mathematics Subject Classification: Primary: 60F10, 60J60; Secondary:
91B70.
Keywords and phrases: Large deviations, Freidlin–Wentzell theory, most likely
path.