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  • © 2009

Local Lyapunov Exponents

Sublimiting Growth Rates of Linear Random Differential Equations

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1963)

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Table of contents (4 chapters)

About this book

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
  • ordinary differential equations

Reviews

From the reviews:

“These lecture notes originate from the author's dissertation and provide a self-contained introduction to the notion of local Lyapunov exponents. … provide a beautiful exposition to this partially subtle subject for readers acquainted with the theory of stochastic differential equations. … Great qualities of this book are also the ample bibliography giving a representative state of the large literature in this field and the great amount of instructively worked out examples. … The composition of the text is throughout clear, carefully thought through and harmonic.” (Michael Högele, Zentralblatt MATH, Vol. 1178, 2010)

Authors and Affiliations

  • Allianz Lebensversicherungs - AG, Stuttgart, Germany

    Wolfgang Siegert

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions