On stability and comparison theorems for systems of stochastic differential equations

A. S. Asylgareev

Ufa State Aviation Technical University, Ufa, 450000 Russia

Abstract: We prove comparison theorems for stochastic differential equations (briefly, SDE) with respect to a standard multidimensional Wiener process as well as for components of systems of SDE with respect to a multidimensional Wiener process. The obtained results are applied to the study of the stability with probability 1 of the perturbed solutions to the SDE.

Key words: stability with probability 1, stochastic differential equation, comparison theorem, multidimensional Wiener process, Itô integral, Stratonovich integral.

UDC: 519.2

Received: 26.02.2018
Revised: 26.02.2018
Accepted: 10.10.2018

DOI: 10.33048/mattrudy.2019.22.101

 English version: Siberian Advances in Mathematics, 2019, 29:3, 153–163

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