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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Bibliographic Information

Book Title: Semiclassical Analysis for Diffusions and Stochastic Processes
Authors: Vassili N. Kolokoltsov
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0112488
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2000
Softcover ISBN: 978-3-540-66972-2Published: 27 March 2000
eBook ISBN: 978-3-540-46587-4Published: 03 December 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 356
Topics: Analysis, Probability Theory and Stochastic Processes

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Table of contents (10 chapters)

Front Matter

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