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.
Original languageEnglish
Pages (from-to)60-81
JournalTheory of Probability and its Applications
Volume57
Issue number1
DOIs
StatePublished - 2013

    Research areas

  • Bessel process, Brownian excursion, Brownian meander, boundary-value problem, eigenvalue, Gaussian process, local time, small deviations.

ID: 7375207