Averaging for systems of stochastic equations with random disturbances
type: Item
instance of: scholarly article
zbMATH Open document ID: 0988.60062
author: Yuriy V. Kolomiets
publication date: 2002-03-13T00:00:00Z
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 1718886
zbMATH Keywords: stochastic equation
zbMATH Keywords: small parameter
zbMATH Keywords: sufficient conditions
zbMATH Keywords: weak convergence
MaRDI profile type: Publication
title: Averaging for systems of stochastic equations with random disturbances
published in: Theory of Stochastic Processes
review text: The author considers systems of stochastic equations with a small parameter \(\varepsilon\). The first equations have unbounded drift and coefficients which depend on the small parameter \(\varepsilon\). The second equations are described by Markov diffusion processes with periodic coefficients. Weak convergence of probability measures induced by the first equations to a certain random process is investigated. In the second part of the proof of the main theorem the technique proposed by \textit{S. Ya. Makhno} [Theory Probab. Appl. 44, No. 3, 495-510 (1999); translation from Teor. Veroyatn. Primen. 44, No. 3, 555-572 (1999; Zbl 0969.60062)] is used extensively.
reviewed by: M. P. Moklyachuk
description: scientific article; zbMATH DE number 1718886