7 papers
Small deviations for integrators in terms of Itô--Wiener expansions
Qingsong Wang, A. A. Dorogovtsev
In this paper, we investigate small deviations for a class of Gaussian processes, known as integrators. In general, such processes are non-Markovian and may even fail to be semimar…
The Geometry of Gaussian Random Curves
Qingsong Wang, A. A. Dorogovtsev, K. V. Hlyniana +1
In this paper, we investigate some geometric properties of non-smooth random curves within a stochastic flow. We consider a polygonal line , whic…
Hitting time for one class of Gaussian proccesses
Qingsong Wang, A. A. Dorogovtsev
In this paper we propose the method to find the hitting probabilities for Gaussian integrators. Using second quantization we obtain the sseries representation for such probabilitie…
Universal generalized functionals and finitely absolutely continuous measures on Banach spaces
A. A. Dorogovtsev, Naoufel Salhi
In this paper we collect several examples of convergence of functions of random processes to generalized functionals of those processes. We remark that the limit is always finitely…
Refinements of asymptotics at zero of Brownian self-intersection local times
A. A. Dorogovtsev, N. Salhi
In this article we establish some estimates related to the Gaussian densities and to Hermite polynomials in order to obtain an almost sure estimate for each term of the Itô-Wiener…
Gaussian structure in coalescing stochastic flows
A. A. Dorogovtsev, E. V. Glinynaya
In the paper we consider the point measure that corresponds to Arratia flow. The central limit theorem of the multiple integrals with respect to this measure was obtained.
Basis entropy in Banach spaces
Andrei Dorogovtsev, Mikhail Popov
We introduce and study two notions of entropy in a Banach space X with a normalized Schauder basis . The geometric entropy E(A) of a subset A of X is defined to be the infimum of r…