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Local Lyapunov Exponents

Sublimiting Growth Rates of Linear Random Differential Equations

  • Wolfgang Siegert
Book
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Part of the Lecture Notes in Mathematics book series (LNM, volume 1963)

About this book

Introduction

Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations.
Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.

Keywords

degenerate diffusion exit probabilities metastability random perturbations of dynamical systems stochastic process sublimiting exponential growth rate

Authors and affiliations

  • Wolfgang Siegert
    • 1
  1. 1.Allianz Lebensversicherungs - AGStuttgartGermany

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