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Regular version of the site

Article

Exact Small Deviation Asymptotics for Some Brownian Functionals.

Theory of Probability and Its Applications. 2013. Vol. 57. No. 1. P. 60-81.
Nikitin Ya. Yu., Pusev R.

We find exact small deviation asymptotics with respect to weighted Hilbert norm for some well-known Gaussian processes. Our approach does not assume the knowledge of eigenfunctions of the correspondinge covariance operator. This makes it possible to generalize many previous results in this area. We also obtain ultimate results connected with exact small deviation of Brownian excursion and Brownian meander as well as for Bessel processes and their local times.