Systems of Linear Stochastic Equations

Chapter
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 66)

Abstract

In this chapter we shall study a linear homogeneous system of equations whose coefficients are perturbed by Gaussian white noise \(\dot{\eta}_{i}^{j}(t)\). Necessary and sufficient conditions for the stability and instability for such type of systems are proven. In particular, exact formula for the Lyapunov exponent is found for the system with constant coefficients. The stabilization problem of unstable deterministic systems by additive white noise. Is also considered.

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Mathematics Department, 1150 Faculty/Administration BuildingWayne State UniversityDetroitUSA
  2. 2.Institute for Information Transmission ProblemsRussian Academy of SciensesMoscowRussia

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