OCCUPATION TIME AND EXACT ASYMPTOTICS OF DISTRIBUTIONS OF L-p-FUNCTIONALS OF THE ORNSTEIN-UHLENBECK PROCESSES, p > 0

摘要

The paper proves the results on exact asymptotics of the probabilities P mu{T-1 x integral(T)(0)vertical bar eta gamma(t)vertical bar(p) dtinfinity, for p>0 for Gaussian Markov Ornstein-Uhlenbeck processes eta gamma and also for their conditional versions. The author uses the Laplace method for the occupation time of Markov processes with continuous time. The calculations are given for the case p=2 with the help of the solution of the extremal problem for the action functional.