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Exact small deviation asymptotics for some Brownian functionals. (English. Russian original) Zbl 1278.60072
Theory Probab. Appl. 57, No. 1, 60-81 (2013); translation from Teor. Veroyatn. Primen. 57, No. 1, 98-123 (2012).
Authors’ abstract: We find exact small deviation asymptotics with respect to a weighted Hilbert norm for some well-known Gaussian processes. Our approach does not require knowledge of the 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.

MSC:
60G15 Gaussian processes
60G05 Foundations of stochastic processes
60J60 Diffusion processes
60F10 Large deviations
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