Exact L₂-Small Deviation Asymptotics for Some Brownian Functionals

2011/04/14 by Ya. yu. Nikitin, Nikitin, Ya. yu., R. S. Pusev +1
Mathematics · #34E20 #60G15 #60J55 #60J65 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:34E20 #msc:60G15 #msc:60J55 #msc:60J65

paper · pdf · doi:10.48550/arxiv.1104.2891

26 pages

arxiv created 2011/04/14 · arxiv updated 2011/04/15

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.

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