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Andrey A. Dorogovtsev

Publications and source records attributed to Andrey A. Dorogovtsev.

9 recordsLinked to original sources
arXiv2026

Visitation measures for non-linear iterations with random perturbations

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 measures, which are deterministic measures that allow one to estimate the time spent by the sequence in the neighbourhoods of its partial limits. The results obtained are compared with statements regarding the statistical convergence of the sequence of iterations under study

math.PR↗
arXiv2025

Maximum principle for optimal control of interacting particle system: stochastic flow model

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 introducing a generalized backward stochastic differential equation with interaction. The existence and uniqueness of the solution of this type of equation is proved. We derive the necessary condition that the optimal control should satisfy. As an application, the linear quadratic case is investigated to illustrate the main results.

math.PR↗
arXiv2023

On a stationary random knot

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 changes its topological type at random moments.

math.PR↗
arXiv2018

Stationary points in coalescing stochastic flows on $\mathbb{R}$

This work is devoted to long-time properties of the Arratia flow with drift -- a stochastic flow on $\mathbb{R}$ whose one-point motions are weak solutions to a stochastic differential equation $dX(t)=a(X(t))dt+dw(t)$ that move independently before the meeting time and coalesce at the meeting time. We study special modification of such flow (constructed in \cite{Riabov}) that gives rise to a random dynamical system and thus allows to discuss stationary points. Existence of a unique stationary point is proved in the case of a strictly monotone Lipschitz drift by developing a variant of a pullback procedure. Connections between the existence of a stationary point and properties of a dual flow are discussed.

math.PR↗
arXiv2013

Transformations of Wiener Measure and Orthogonal Expansions

In this paper we study the structure of square integrable functionals measurable with respect to coalescing stochastic flows. The case of $L^2$ space generated by the process $η(\cdot)=w(\min(τ,\cdot)),$ where $w$ is a Brownian motion and $τ$ is the first moment when $w$ hits the given continuous function $g$ is considered. We present a new construction of multiple stochastic integrals with respect to the process $η.$ Our approach is based on the change of measure technique. The analogue of the Itô-Wiener expansion for the space $L^2(η)$ is constructed.

math.PR↗
arXiv2011

On regularization of formal Fourier--Wiener transform of the self-intersection local time of planar Gaussian process

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 of regularization we use in this work related to regularization of functions with non-integrable singularities. The strong local nondeterminism property, which is more restrictive than the property of local nondeterminism introduced by S.Berman is considered. Its geometrical meaning in the construction of the regularization is investigated. As the example the problem of regularization is solved for the compact perturbation of the planar Wiener process.

math.PR↗
arXiv2010

Semigroups of finite-dimensional random projections

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 the asymptotic behavior of the widths of compact subsets with respect to the subspaces generated by the semigroup operators.

math.PR↗