Exact L_2-Small Deviation Asymptotics for Some Brownian Functionals

摘要

We find exact small deviation asymptotics with respect to weighted Hilbertnorm for some well-known Gaussian processes. Our approach does not require theknowledge of eigenfunctions of the covariance operator of a weighted process.Such a peculiarity of the method makes it possible to generalize many previousresults in this area. We also obtain new relations connected to exact smalldeviation asymptotics for a Brownian excursion, a Brownian meander, and Besselprocesses and bridges.