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100   $a20100730d2000      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aSemiclassical Analysis for Diffusions and Stochastic Processes /$fby Vassili N. Kolokoltsov
205   $a1st ed. 2000.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2000.
215   $a1 online resource (VIII, 356 p.) 
225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v1724
300   $aIncludes index.
311 08$a3-540-66972-8 
327   $aGaussian diffusions -- Boundary value problem for Hamiltonian systems -- Semiclassical approximation for regular diffusion -- Invariant degenerate diffusion on cotangent bundles -- Transition probability densities for stable jump-diffusions -- Semiclassical asymptotics for the localised Feller-Courrège processes -- Complex stochastic diffusion or stochastic Schrödinger equation -- Some topics in semiclassical spectral analysis -- Path integration for the Schrödinger, heat and complex diffusion equations.
330   $aThe monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by stable Lévy processes, (iii) complex stochastic Schrödinger equations which correspond to models of quantum open systems. The main results of the book concern the existence, two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the transition probability densities of the corresponding random process. The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed. Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus. .
410  0$aLecture Notes in Mathematics,$x1617-9692 ;$v1724
606   $aMathematical analysis
606   $aProbabilities
606   $aAnalysis
606   $aProbability Theory
615  0$aMathematical analysis.
615  0$aProbabilities.
615 14$aAnalysis.
615 24$aProbability Theory.
676   $a519.23
700   $aKolokoltsov$b Vassili N$4aut$4http://id.loc.gov/vocabulary/relators/aut$0441084
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910146313503321
996   $aSemiclassical analysis for diffusions and stochastic processes$978817
997   $aUNINA