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- Publisher
- de Gruyter
- Copyright
- Copyright © 2009 Walter de Gruyter
- ISSN
- 0926-6364
- eISSN
- 1569-397X
- DOI
- 10.1515/rose.1993.1.2.151
- Publisher site
- See Article on Publisher Site
Abstract
Random Oper. & Stock. Equ., Vol. 1, No. 2, pp. 151-160 (1993) © VSP 1993 V. V. ANISIMOV Department of Cybernetics, Kyjiv University, Kyjiv, 252017, Ukraine Received for ROSE 15 March 1991 Abstract--The results of the averaging principle type on convergence of the trajectory of switching process to the solution of a differential equation are obtained in case switchings accumulating asymptotically. Some applications to the stochastic networks and branching processes are considered. The class of switching processes (SP) was introduced in [1--4]. The limit theorems on convergence of SP, in case the number of switchings on the considered interval of time do not increase asymptotically were studied in [3, 4], In this paper we obtain the result of the type of averaging principle on convergence of the trajectory SP to the solution of a differential equation in case switchings accumulating asymptotically. We introduce the class of S P in the following way. Let, for every positive n, the independent families 3nk = {(fn*(M,a),r nfc (x,a)): t 2 , G , R m }, k ^ 0, be given, where X is some space with the -algebra 3, £ n fc(*? £> a), t ^ 0, is a random
Journal
Random Operators and Stochastic Equations – de Gruyter
Published: Jan 1, 1993