Exact L_2-Small Deviation Asymptotics for Some Brownian Functionals

Details Exact L_2-Small Deviation Asymptotics for Some Brownian Functionals Exact L_2-Small Deviation Asymptotics for Some Brownian Functionals

2011-04-14

arxiv.org/abs/1104.2891v1

Mathematics

Probability

26 pages

Scientific paper

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.

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