Exact L_2-Small Deviation Asymptotics for Some Brownian Functionals
Probability
2011-04-15 v1
Abstract
We find exact small deviation asymptotics with respect to weighted Hilbert norm for some well-known Gaussian processes. Our approach does not require the knowledge of eigenfunctions of the covariance operator of a weighted process. Such a peculiarity of the method makes it possible to generalize many previous results in this area. We also obtain new relations connected to exact small deviation asymptotics for a Brownian excursion, a Brownian meander, and Bessel processes and bridges.
Cite
@article{arxiv.1104.2891,
title = {Exact L_2-Small Deviation Asymptotics for Some Brownian Functionals},
author = {Ya. yu. Nikitin and R. S. Pusev},
journal= {arXiv preprint arXiv:1104.2891},
year = {2011}
}
Comments
26 pages