Research output: Contribution to journal › Article
Exact Small Deviation Asymptotics for Some Brownian Functionals. / Nikitin, Y.Y.; Pusev, R.S.
In: Theory of Probability and its Applications, Vol. 57, No. 1, 2013, p. 60-81.Research output: Contribution to journal › Article
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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 -
ID: 7375207