Semiclassical Analysis for Diffusions and Stochastic Processes

By:

Vassili N Kolokoltsov

Format:

Paperback / softback

Series:

Lecture Notes in Mathematics

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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.

Release date Australia

March 27th, 2000

Author

Vassili N Kolokoltsov

Audiences

Postgraduate, Research & Scholarly
Professional & Vocational

Illustrations

VIII, 356 p.

Pages

356

Series

Lecture Notes in Mathematics

Dimensions

156x234x19

ISBN-13

9783540669722

Product ID

2813259

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