Semiclassical Analysis for Diffusions and Stochastic Processes (Lecture Notes in Mathematics, 1724) - Softcover

Kolokoltsov, Vassili N.

 
9783540669722: Semiclassical Analysis for Diffusions and Stochastic Processes (Lecture Notes in Mathematics, 1724)
Softcover
ISBN 10: 3540669728 ISBN 13: 9783540669722
Publisher: Springer, 2000

Synopsis

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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Publisher
Springer
Publication date
2000
Language
English
ISBN 10 
3540669728
ISBN 13 
9783540669722
Binding
Paperback
Number of pages
364