Semiclassical Analysis for Diffusions and Stochastic Processes
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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 L vy processes, (iii) complex stochastic Schr dinger 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.
Format:Paperback
Language:English
ISBN:3540669728
ISBN13:9783540669722
Release Date:March 2000
Publisher:Springer
Length:356 Pages
Weight:1.12 lbs.
Dimensions:0.7" x 6.2" x 9.3"
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