Exact asymptotics of Laplace-type Wiener integrals for Lp-functionals

被引：6
|
作者：
Fatalov, V. R. [1 ]
机构：
[1] Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow, Russia
来源：
IZVESTIYA MATHEMATICS | 2010年 / 74卷 / 01期
关键词：
large deviation; Gaussian process; Markov process; occupation time; covariance operator; generating operator; Schrodinger operator; hypergeometric function; GAUSSIAN-PROCESSES; LARGE DEVIATIONS; MINIMUM POINTS; MARKOV PROCESS; ABSOLUTE VALUE; P-GREATER-THAN-0; DISTRIBUTIONS; PROBABILITIES; TIME; NORM;
D O I：
10.1070/IM2010v074n01ABEH002485
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove theorems on the exact asymptotic behaviour of the integrals E exp{u(integral(1)(0)|xi(t)|(p) dt)(alpha/p)}, E exp{-u integral(1)(0)|xi(t)|(p) dt}, u --> infinity, for p > 0 and 0 < alpha < 2 for two random processes xi(t), namely, the Wiener process and the Brownian bridge, and obtain other related results. Our approach is via the Laplace method for infinite-dimensional distributions, namely, Gaussian measures and the occupation time for Markov processes.
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页码：189 / 216
页数：28
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