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Birkhäuser

Schrödinger Diffusion Processes

  • Book
  • © 1996

Overview

Authors:
  1. Robert Aebi

    1. Institut für Mathematische Statistik und Versicherungslehre, Universität Bern, Bern, Switzerland

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Part of the book series: Probability and Its Applications (PA)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. Schrödinger’s View of Natural Laws

    • Robert Aebi
    Pages 1-22

  3. Diffusions with Singular Drift

    • Robert Aebi
    Pages 23-54

  4. Integral and Diffusion Equations

    • Robert Aebi
    Pages 55-76

  5. Itô’s Formula for Non-Smooth Functions

    • Robert Aebi
    Pages 77-89

  6. Large Deviations

    • Robert Aebi
    Pages 91-114

  7. Interacting Diffusion Processes

    • Robert Aebi
    Pages 115-150

  8. Schrödinger Systems

    • Robert Aebi
    Pages 151-173

  9. Back Matter

    Pages 175-188
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Keywords

About this book

In 1931 Erwin Schrödinger considered the following problem: A huge cloud of independent and identical particles with known dynamics is supposed to be observed at finite initial and final times. What is the "most probable" state of the cloud at intermediate times? The present book provides a general yet comprehensive discourse on Schrödinger's question. Key roles in this investigation are played by conditional diffusion processes, pairs of non-linear integral equations and interacting particles systems. The introductory first chapter gives some historical background, presents the main ideas in a rather simple discrete setting and reveals the meaning of intermediate prediction to quantum mechanics. In order to answer Schrödinger's question, the book takes three distinct approaches, dealt with in separate chapters: transformation by means of a multiplicative functional, projection by means of relative entropy, and variation of a functional associated to pairs of non-linear integral equations. The book presumes a graduate level of knowledge in mathematics or physics and represents a relevant and demanding application of today's advanced probability theory.

Authors and Affiliations

  • Institut für Mathematische Statistik und Versicherungslehre, Universität Bern, Bern, Switzerland

    Robert Aebi

Bibliographic Information

  • Book Title: Schrödinger Diffusion Processes

  • Authors: Robert Aebi

  • Series Title: Probability and Its Applications

  • DOI: https://doi.org/10.1007/978-3-0348-9027-4

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag Basel 1996

  • Hardcover ISBN: 978-3-7643-5386-5Due: 29 February 1996

  • Softcover ISBN: 978-3-0348-9874-4Published: 04 October 2011

  • eBook ISBN: 978-3-0348-9027-4Published: 06 December 2012

  • Series ISSN: 2297-0371

  • Series E-ISSN: 2297-0398

  • Edition Number: 1

  • Number of Pages: 186

  • Topics: Probability Theory and Stochastic Processes, Applications of Mathematics

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