000 04109nam a22004815i 4500
001 978-3-642-25847-3
003 DE-He213
005 20140220083307.0
007 cr nn 008mamaa
008 120530s2012 gw | s |||| 0|eng d
020 _a9783642258473
_9978-3-642-25847-3
024 7 _a10.1007/978-3-642-25847-3
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aFreidlin, Mark I.
_eauthor.
245 1 0 _aRandom Perturbations of Dynamical Systems
_h[electronic resource] /
_cby Mark I. Freidlin, Alexander D. Wentzell.
250 _a3rd ed. 2012.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2012.
300 _aXXVIII, 458 p. 48 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v260
505 0 _a1.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 _aMany 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 _aMathematics.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
700 1 _aWentzell, Alexander D.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642258466
830 0 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v260
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-25847-3
912 _aZDB-2-SMA
999 _c102497
_d102497