Abstract
Abstract In this brief survey, we are concerned with the problem of stability of differential equations with randomly fluctuating parameters. Even for this specific problem, we can cover only a small portion of the available results. The increased interest on this topic has generated a vast literature. Thus, we can only touch upon a few of the significant results and techniques. We distinguish between stochastic equations with Gaussian white noise coefficients, and stochastic equations with (non-white) physical noise coefficients. We discuss a few problems for which results are available, but complete answers have not been forthcoming as yet. We treat, mainly, stochastic ordinary differential equations. However, we have also included a brief discussion of stochastic functional equations as well as discrete time stochastic equations. Functional equations are of interest in applications to materials with memory and to control of complex multicomponent structures. Discrete time equations are of interest as on-line computer models of identification algorithms.
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