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Lambros Katafygiotis, Yevgeny Tsarkov, "Averaging and stability of quasilinear functional differential equations with Markov parameters", International Journal of Stochastic Analysis, vol. 12, Article ID 490250, 15 pages, 1999. https://doi.org/10.1155/S1048953399000015
Averaging and stability of quasilinear functional differential equations with Markov parameters
Abstract
An asymptotic method for stability analysis of quasilinear functional differential equations, with small perturbations dependent on phase coordinates
and an ergodic Markov process, is presented. The proposed method is
based on an averaging procedure with respect to: 1) time along critical
solutions of the linear equation; and 2) the invariant measure of the
Markov process. For asymptotic analysis of the initial random equation
with delay, it is proved that one can approximate its solutions (which are
stochastic processes) by corresponding solutions of a specially constructed
averaged, deterministic ordinary differential equation. Moreover, it is
proved that exponential stability of the resulting deterministic equation is
sufficient for exponential
Copyright
Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
