E. S. Palamarchuk, “On asymptotic behavior of solutions of multivariate linear stochastic differential equations with multiplicative noise”, Teor. Veroyatnost. i Primenen., 2024, Volume 69, Issue 3,Pages <nobr>472

This article is cited in 1 paper

On asymptotic behavior of solutions of multivariate linear stochastic differential equations with multiplicative noise

E. S. Palamarchuk^ab

^a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
^b National Research University Higher School of Economics, Moscow

Abstract: We study asymptotic behavior of solutions of linear multidimensional stochastic differential equations (SDEs) with time-varying coefficients. The case of SDEs under multiplicative noise and random input is considered. We obtain closed-form functions majorizing solutions of SDEs almost surely and in the mean-square sense. As applications, we consider systems involving additive noise and examine a motion model of interrelated objects.

Keywords: inhomogeneous linear stochastic differential equations, upper function, multiplicative noise.

Received: 23.09.2023
Revised: 30.04.2024
Accepted: 10.05.2024

DOI: 10.4213/tvp5682