Random Perturbations of Dynamical Systems

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 s...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Freidlin, Mark I. (Συγγραφέας), Wentzell, Alexander D. (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
Έκδοση:3rd ed. 2012.
Σειρά:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 260
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
LEADER 04096nam a22004815i 4500
001 978-3-642-25847-3
003 DE-He213
005 20151121052650.0
007 cr nn 008mamaa
008 120530s2012 gw | s |||| 0|eng d
020 |a 9783642258473  |9 978-3-642-25847-3 
024 7 |a 10.1007/978-3-642-25847-3  |2 doi 
040 |d GrThAP 
050 4 |a QA273.A1-274.9 
050 4 |a QA274-274.9 
072 7 |a PBT  |2 bicssc 
072 7 |a PBWL  |2 bicssc 
072 7 |a MAT029000  |2 bisacsh 
082 0 4 |a 519.2  |2 23 
100 1 |a Freidlin, Mark I.  |e author. 
245 1 0 |a Random Perturbations of Dynamical Systems  |h [electronic resource] /  |c by Mark I. Freidlin, Alexander D. Wentzell. 
250 |a 3rd ed. 2012. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg :  |b Imprint: Springer,  |c 2012. 
300 |a XXVIII, 460 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,  |x 0072-7830 ;  |v 260 
505 0 |a 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 Perturbations of Hamiltonian Systems -- 9. The Multidimensional Case -- 10.Stability Under Random Perturbations -- 11.Sharpenings and Generalizations -- References -- Index. 
520 |a 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. 
650 0 |a Mathematics. 
650 0 |a Probabilities. 
650 1 4 |a Mathematics. 
650 2 4 |a Probability Theory and Stochastic Processes. 
700 1 |a Wentzell, Alexander D.  |e author. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783642258466 
830 0 |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,  |x 0072-7830 ;  |v 260 
856 4 0 |u http://dx.doi.org/10.1007/978-3-642-25847-3  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)