Semiclassical Analysis for Diffusions and Stochastic Processes: 1724 - Brossura

Kolokoltsov, Vassili N.

 
9783540669722: Semiclassical Analysis for Diffusions and Stochastic Processes: 1724
Brossura
ISBN 10: 3540669728 ISBN 13: 9783540669722
Casa editrice: Springer Berlin Heidelberg, 2010

Sinossi

The 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.       




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Contenuti

Gaussian 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.

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Editore
Springer Berlin Heidelberg
Data di pubblicazione
2010
Lingua
Inglese
ISBN 10 
3540669728
ISBN 13 
9783540669722
Rilegatura
Copertina flessibile
Numero di pagine
364
Contatto del produttore
non disponibile
Persona responsabile
ProductSafety@springernature.com
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