TY - JOUR

T1 - Exact Small Deviation Asymptotics for Some Brownian Functionals

AU - Nikitin, Y.Y.

AU - Pusev, R.S.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Bessel process

KW - Brownian excursion

KW - Brownian meander

KW - boundary-value problem

KW - eigenvalue

KW - Gaussian process

KW - local time

KW - small deviations.

U2 - 10.1137/S0040585X97985790

DO - 10.1137/S0040585X97985790

M3 - Article

VL - 57

SP - 60

EP - 81

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 1

ER -