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Lyapunov Exponents and Stochastic Flows of Linear and Affine Hereditary Systems

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Diffusion Processes and Related Problems in Analysis, Volume II

Part of the book series: Progress in Probability ((PRPR,volume 27))

Abstract

In this article we intend to review known results—and also discuss new ones—concerning the existence of flows and the characterization of Lyapunov exponents for trajectories of stochastic linear and affine hereditary systems. Such systems (also called stochastic functional differential equations) are stochastic differential equations in which the differential of the state variable x depends on its current value x(t) at time t as well as its previous values x(s), t − r ≤ s < t. We shall be concerned almost exclusively with the finite history case 0 ≤ r < ∞.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Southern Illinois University, Carbondale, IL, 62901

    Salah-Eldin A. Mohammed

  2. Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA, 15213-3890

    Salah-Eldin A. Mohammed

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  1. Salah-Eldin A. Mohammed
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Editors and Affiliations

  1. Department of Mathematics, Northwestern University, Evanston, IL, 60208, USA

    Mark A. Pinsky

  2. Department of Mathematics, University of North Carolina, Charlotte, N.C., 28223, USA

    Volker Wihstutz

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Mohammed, SE.A. (1992). Lyapunov Exponents and Stochastic Flows of Linear and Affine Hereditary Systems. In: Pinsky, M.A., Wihstutz, V. (eds) Diffusion Processes and Related Problems in Analysis, Volume II. Progress in Probability, vol 27. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0389-6_7

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  • DOI: https://doi.org/10.1007/978-1-4612-0389-6_7

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6739-3

  • Online ISBN: 978-1-4612-0389-6

  • eBook Packages: Springer Book Archive

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