ENGLISH

Semiclassical Analysis for Diffusions and Stochastic Processes

By Vassili N. Kolokoltsov (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2000
ISBN
9783540669722, 3-540-66972-8
DOI
10.1007/BFb0112488
ISSN
0075-8434
Open Library ID
OL15476423M
Language
english
Format
PDF
Filesize
16 MB (16891943 bytes)
Series
Lecture Notes in Mathematics 1724
Edition
1
Pages
356\360
Library
mexmat
Time added
2009-07-20 03:45:11
Analysis; Probability Theory and Stochastic Proces

Description

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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