Nikitin, Ya. Yu.; Pusev, R. S. 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. Reviewer: Nikolai N. Leonenko (Cardiff) Cited in 10 Documents MSC: 60G15 Gaussian processes 60G05 Foundations of stochastic processes 60J60 Diffusion processes 60F10 Large deviations Keywords:Bessel process; small deviations; Gaussian process; Brownian excursion; Brownian meander; Karhunen-Loève expansion PDFBibTeX XMLCite \textit{Ya. Yu. Nikitin} and \textit{R. S. Pusev}, Theory Probab. Appl. 57, No. 1, 60--81 (2013; Zbl 1278.60072); translation from Teor. Veroyatn. Primen. 57, No. 1, 98--123 (2012) Full Text: DOI arXiv