22 citations · 35 across the 19 of their papers we have counts for
21 papers · 1 filter
Visitation measures for non-linear iterations with random perturbations
Andrey A. Dorogovtsev, Iryna Nishchenko
A sequence of non-linear iterations with non-identically distributed random perturbations is studied. The asymptotic behaviour of the sequence is described via its visitations meas…
Large deviation principle for generalized multiple intersection local times of multidimensional Brownian motion
Andrey A. Dorogovtsev, Naoufel Salhi
In this paper we consider examples of positive generalized Wiener functions and we establish a large deviation principle for the generalized multiple intersection local time of the…
Maximum principle for optimal control of interacting particle system: stochastic flow model
Andrey A. Dorogovtsev, Yuecai Han, Kateryna Hlyniana +1
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by i…
Intermittency Phenomena for Mass Distributions of Stochastic Flows with Interaction
Andrey Dorogovtsev, Alexander Weiß
The intermittency phenomenon is the occurrence of very high but rare peaks, which despite their rarity influence the asymptotic behaviour of the underlying system. Mathematically t…
On a stationary random knot
Andrey A. Dorogovtsev
In this article the construction of a stationary random knot is proposed. The corresponding smooth random curve has no self-intersections in deterministic moments of time and chang…
On 1-point densities for Arratia flows with drift
A. A. Dorogovtsev, M. B. Vovchanskyi
We show that if drift coefficients of Arratia flows converge in or then the 1-point densities associated with these flows converge to the density for the f…
Self-intersection local times of random fields in stochastic flows
Andrey Dorogovtsev, Alexander Gnedin, Olga Izyumtseva
In this article we study transformations of Gaussian field by stochastic flow on the plane. A stochastic flow is a solution to the equation with interaction whose coefficients depe…
Stationary points in coalescing stochastic flows on
Andrey A. Dorogovtsev, Georgii V. Riabov, Björn Schmalfuß
This work is devoted to long-time properties of the Arratia flow with drift -- a stochastic flow on whose one-point motions are weak solutions to a stochastic differen…
Clark formula for local time for one class of Gaussian processes
Andrey Dorogovtsev, Olga Izyumtseva, Georgii Riabov +1
In the article we present chaotic decomposition and analog of the Clark formula for the local time of Gaussian integrators. Since the integral with respect to Gaussian integrator i…
The rate of weak convergence of the n-point motions of Harris flows
A. A. Dorogovtsev, V. V. Fomichov
In this paper we discuss the Wasserstein distance between the n-point motions of Harris flows whose covariance functions have compact support. We prove that it can be estimated by…
On self-intersection local times for generalized Brownian bridges and the distance between step functions
A. A. Dorogovtsev, O. L. Izyumtseva
In the paper -multiple self-intersection local time for planar Gaussian integrators generated by linear operator with nontrivial kernel is studied. In this case additional singu…
Properties of Gaussian local times
Andrey Dorogovtsev, Olga Iziumtseva
In the paper we investigate the local times for Gaussian integrators. Every Gaussian integrator can be associated with the continuous linear operator in the space of square integra…
Transformations of Wiener Measure and Orthogonal Expansions
Andrey A. Dorogovtsev, Georgii V. Riabov
In this paper we study the structure of square integrable functionals measurable with respect to coalescing stochastic flows. The case of space generated by the process $η(\c…
Multiplicative white noise functionals and the Krylov-Veretennikov expansion for coalescing stochastic flows
Andrey A. Dorogovtsev
In this article we consider multiplicative operator-valued white noise functionals related to a stochastic flow. A generalization of the Krylov-Veretennikov expansion is presented.…
On regularization of formal Fourier--Wiener transform of the self-intersection local time of planar Gaussian process
Andrey A. Dorogovtsev, Olga L. Izumtseva
Fourier-Wiener transform of the formal expression for multiple self-intersection local time is described in terms of the integral, which is divergent on the diagonals. The method o…
Semigroups of finite-dimensional random projections
Andrey A. Dorogovtsev
In this paper we present a complete description of a stochastic semigroup of finite-dimensional projections in Hilbert space. The geometry of such semigroups is characterized by th…
Stochastic anticipating boundary value problems
Andrey A Dorogovtsev
This article is devoted to the stochastic anticipating equations with the extended stochastic integral with respect to the Gaussian processes of a special type. In the particular c…
One Brownian Stochastic Flow
Andrey A Dorogovtsev
The weak limits of the measure-valued processes organized as a mass carried by the interacting Brownian particles are described. As a limiting flow the Arrattia flow is obtained.
Smoothing problem in anticipating scenario
Andrey A Dorogovtsev
This article is devoted to the stochastic anticipating equations with the extended stochastic integral with respect to the Gaussian processes of a special type and its application…
One version of the Clark representation theorem for Arratia flow
Andrey A Dorogovtsev
The article contains description of the functionals from the family of coalescing Brownian particles. New type of the stochastic integral is introduced and used.
On random measures on the space of trajectories and strong and weak solutions of stochastic equations
A. A. Dorogovtsev
The random measures on the space of continuous functions are considered. Stationary random measures are described. The weak solutions of the stochastic equations are substituted by…