Grundlehren der mathematischen Wissenschaften

Fluctuations in Markov Processes

Time Symmetry and Martingale Approximation

Authors: Komorowski, Tomasz, Landim, Claudio, Olla, Stefano

  • Unique in mathematical literature covers the most advanced theories about martingale approach to central limit theorems
  • Develops techniques that allow to deal with applications in statistical mechanics and engineering
  • Is of interest to probabilists, mathematical physicists and analysts
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About this book

The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior).
 
There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest also to mathematical physicists and analysts.

Reviews

From the reviews:

“The authors provide a monographic survey of the martingale approximation for additive functionals of Markov processes and central limit theorems (CLTs) and invariance principles following from this. … Each chapter closes with a section of historical and bibliographical comments. … these historical surveys make the book a long-lasting source of information about development of ideas, related fields and results, and historical data. The book is highly recommended to researchers and postgraduate students working in various fields of interacting particle systems, random environments and homogenization.” (Bálint Tóth, Mathematical Reviews, November, 2013)

Table of contents (14 chapters)

  • A Warming-Up Example

    Komorowski, Tomasz (et al.)

    Pages 3-32

  • Central Limit Theorems

    Komorowski, Tomasz (et al.)

    Pages 33-79

  • Random Walks in Random Environment

    Komorowski, Tomasz (et al.)

    Pages 81-135

  • Bounds and Variational Principles for the Asymptotic Variance

    Komorowski, Tomasz (et al.)

    Pages 137-151

  • The Simple Exclusion Process

    Komorowski, Tomasz (et al.)

    Pages 155-197

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-29880-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-642-29879-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-642-42847-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Fluctuations in Markov Processes
Book Subtitle
Time Symmetry and Martingale Approximation
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
345
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-29880-6
DOI
10.1007/978-3-642-29880-6
Hardcover ISBN
978-3-642-29879-0
Softcover ISBN
978-3-642-42847-0
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XVIII, 494
Topics