Integrals of Bessel processes and multi-dimensional Ornstein–Uhlenbeck processes: exact asymptotics for -functionals

Abstract

We prove results on exact asymptotics of the expectations , as for , , , where , , is a Bessel process of order . We also find exact asymptotics of the probabilities , as , where , , is the -dimensional non- stationary Ornstein– Uhlenbeck process with a parameter starting at the origin. We also obtain a number of other results. Numerical values of the asymptotics are given for , .