Random perturbations of dynamical systems

Various limit theorems for stochastic processes defined as a result of randomperturbations of dynamical systems are considered. Exit problems, metastability and its manifestations such as stochastic resonance, optimal stabilisation,and the asymptotics of stationary distributions are presented in detail. Notions of quasi-potential are introduced and transition paths are described. The authors' main tools are the large deviation theory, the central limit theorem for stochastic processes, and the averaging principle. The results allow us tomake explicit calculations of the asymptotics of many interesting characteristics of the perturbed system. Most of these results are closely connected withPDEs. This new edition contains more details on quasi-potential, expansions of the averaging principle, and a new chapter on random perturbations of Hamiltonian systems with many degrees of freedom, along with new results on fast oscillating perturbations of systems with conservation laws. The results on random perturbations shed light on classical problems concerning deterministic perturbations of Hamiltonian systems. New findings on wave front propagation in semilinear PDEs and on random perturbations of certain infinite-dimensional dynamical systems have been incorporated into the chapter on sharpenings and generalizations. Third revised and enlarged edition. New chapters and enlarged bibliographic references. A very detailed and deep mathematical treatment of the long termbehavior of randomly perturbed dynamical systems. INDICE: 1.Random Perturbations. 2.Small Random Perturbations on a Finite Time Interval. 3.Action Functional. 4.Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point. 5.Perturbations Leading to Markov Processes. 6.Markov Perturbations on Large Time Intervals. 7.The Averaging Principle. Fluctuations in Dynamical Systems with Averaging. 8.Random Perturbationsof Hamiltonian Systems. 9. The Multidimensional Case. 10.Stability Under Random Perturbations. 11.Sharpenings and Generalizations. References. Index.

• ISBN: 978-3-642-25846-6
• Editorial: Springer Berlin Heidelberg
• Encuadernacion: Cartoné
• Páginas: 500
• Fecha Publicación: 30/04/2012
• Nº Volúmenes: 1
• Idioma: Inglés