Lecture Notes in Mathematics: Sublimiting Growth Rates of Linear Random Differential Equations

Siegert, Wolfgang

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.

Details

Published by: Springer

Publication Date: 2008-11-13

Format: Paperback

ISBN-13: 9783540859635

DOI: 10.1007/978-3-540-85964-2

Dimensions: 235cm x155cm

Pages: 254