Semiclassical Analysis for Diffusions and Stochastic Processes

  • Authors
  • Vassili N. Kolokoltsov

Part of the Lecture Notes in Mathematics book series (LNM, volume 1724)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Vassili N. Kolokoltsov
    Pages 1-16
  3. Vassili N. Kolokoltsov
    Pages 17-39
  4. Vassili N. Kolokoltsov
    Pages 40-96
  5. Vassili N. Kolokoltsov
    Pages 97-135
  6. Vassili N. Kolokoltsov
    Pages 136-145
  7. Vassili N. Kolokoltsov
    Pages 239-254
  8. Back Matter
    Pages 280-352

About this book

Introduction

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.

Keywords

Boundary value problem Lévy process Markov process Markov processes Stochastic Hamilton-Jacobi and Schröder equations Stochastic processes diffusion path integral semiclassical approximation stochastic process

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0112488
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66972-2
  • Online ISBN 978-3-540-46587-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book