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Random Perturbations of Dynamical Systems (Paperback, 3rd ed. 2012)
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Random Perturbations of Dynamical Systems (Paperback, 3rd ed. 2012)
Series: Grundlehren der mathematischen Wissenschaften, 260
Expected to ship within 10 - 15 working days
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Many notions and results presented in the previous editions of this
volume have since become quite popular in applications, and many of
them have been "rediscovered" in applied papers. In the present 3rd
edition small changes were made to the chapters in which long-time
behavior of the perturbed system is determined by large deviations.
Most of these changes concern terminology. In particular, it is
explained that the notion of sub-limiting distribution for a given
initial point and a time scale is identical to the idea of
metastability, that the stochastic resonance is a manifestation of
metastability, and that the theory of this effect is a part of the
large deviation theory. The reader will also find new comments on
the notion of quasi-potential that the authors introduced more than
forty years ago, and new references to recent papers in which the
proofs of some conjectures included in previous editions have been
obtained. Apart from the above mentioned changes the main
innovations in the 3rd edition concern the averaging principle. A
new Section on deterministic perturbations of one-degree-of-freedom
systems was added in Chapter 8. It is shown there that pure
deterministic perturbations of an oscillator may lead to a
stochastic, in a certain sense, long-time behavior of the system,
if the corresponding Hamiltonian has saddle points. The usefulness
of a joint consideration of classical theory of deterministic
perturbations together with stochastic perturbations is illustrated
in this section. Also a new Chapter 9 has been inserted in which
deterministic and stochastic perturbations of systems with many
degrees of freedom are considered. Because of the resonances,
stochastic regularization in this case is even more important.
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