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Semiclassical Analysis for Diffusions and Stochastic Processes

  • Book
  • © 2000

Overview

Authors:
  1. Vassili N. Kolokoltsov
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1724)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    • Vassili N. Kolokoltsov
    Pages 1-16

  3. Gaussian diffusions

    • Vassili N. Kolokoltsov
    Pages 17-39

  4. Boundary value problem for Hamiltonian systems

    • Vassili N. Kolokoltsov
    Pages 40-96

  5. Semiclassical approximation for regular diffusion

    • Vassili N. Kolokoltsov
    Pages 97-135

  6. Invariant degenerate diffusion on cotangent bundles

    • Vassili N. Kolokoltsov
    Pages 136-145

  7. Transition probability densities for stable jump-diffusions

    • Vassili N. Kolokoltsov
    Pages 146-190

  8. Semiclassical asymptotics for the localised Feller-Courrège processes

    • Vassili N. Kolokoltsov
    Pages 191-222

  9. Complex stochastic diffusion or stochastic Schrödinger equation

    • Vassili N. Kolokoltsov
    Pages 223-238

  10. Some topics in semiclassical spectral analysis

    • Vassili N. Kolokoltsov
    Pages 239-254

  11. Path integration for the Schrödinger, heat and complex diffusion equations

    • Vassili N. Kolokoltsov
    Pages 255-279

  12. Back Matter

    Pages 280-352
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Keywords

About this book

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.       





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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