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  • © 2000

Semiclassical Analysis for Diffusions and Stochastic Processes

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
  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. Some topics in semiclassical spectral analysis

    • Vassili N. Kolokoltsov
    Pages 239-254
  8. Back Matter

    Pages 280-352

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.       





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

  • 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

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions