English

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.

Keywords

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

R2 v1 2026-06-21T17:54:19.860Z