Speciality:
01.01.05 (Probability theory and mathematical statistics)
E-mail: Website: https://sites.google.com/site/mlprobability Keywords: random processes,
Gaussian processes,
local times,
small deviations,
large deviations,
functional laws,
limit theorems.
Subject:
Necessary conditions were found for the existence of local times of sample paths of Gaussian processes. A class of stationary processes which do not have local time was discovered. A fiber method was developed for study of distributions of stochastic functionals. of the processes with independent increments. Necessary and sufficient conditions for validity of the functional law of iterated logarithm for Wiener process with respect to arbitrary norm were found.New almost sure limit theorems were found for sums of independent variables and for martingales. The small ball probabilities were investigated for Wiener process with respect to weighted norms as well as their applications to analytic properties of Volterra operators.
Main publications:
Gaussian Random Functions, 1995, Kluwer, Dordrecht, 330 p.
Local Properties of Distributions of Stochastic Functionals (joint with Yu. A. Davydov and N. V. Smorodina), 1997, ser. Translations of Mathematical Monographs, v. 173, AMS, Providence 184 p.
On the lower tail probabilities of some random series, Ann. Probab., 1997, 25, 424–442.
On almost sure limit theorems (joint with I. A. Ibragimov). Theor. Probab. Appl., 1999, 44, 254–272.
Approximation and entropy numbers of Volterra operators with application to Brownian Motion (joint with W. Linde). Memoirs of Amer. Math. Soc., 2002. 80 p.
