Stochastic Tools in Mathematics and Science

  • Alexandre Chorin
  • Ole H. Hald

Part of the Surveys and Tutorials in the Applied Mathematical Sciences book series (STAMS, volume 1)

Table of contents

  1. Front Matter
    Pages 1-9
  2. Alexandre J. Chorin, Ole H. Hald
    Pages 1-17
  3. Alexandre J. Chorin, Ole H. Hald
    Pages 19-46
  4. Alexandre J. Chorin, Ole H. Hald
    Pages 47-81
  5. Alexandre J. Chorin, Ole H. Hald
    Pages 83-107
  6. Alexandre J. Chorin, Ole H. Hald
    Pages 109-134
  7. Alexandre J. Chorin, Ole H. Hald
    Pages 135-159
  8. Back Matter
    Pages 1-2

About this book

Introduction

Stochastic Tools in Mathematics and Science is an introductory book on probability-based modeling. It covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. The topics covered include conditional expectations, stochastic processes, Brownian motion and its relation to partial differential equations, Langevin equations, the Liouville and Fokker-Planck equations, as well as Markov chain Monte Carlo algorithms, renormalization and dimensional reduction, and basic equilibrium and non-equilibrium statistical mechanics. The applications include data assimilation, prediction from partial data, spectral analysis, and turbulence. A noteworthy feature of the book is the systematic analysis of memory effects.

In this second edition, the new topics include Feynman diagrams and a new discussion of the renormalization group.

The book is based on lecture notes from a class that has attracted graduate and advanced undergraduate students from mathematics and from many other science departments at the University of California, Berkeley. Each chapter is followed by exercises. The book will be useful for scientists and engineers working in a wide range of fields and applications.

"Chorin and Hald provide excellent explanations with considerable insight and deep mathematical understanding, especially toward the end of the book in the context of simplified versions of the famous statistical mechanics models of Ising and of Mori and Zwanzig."

(SIAM Review)

Keywords

Brownian motion Chorin Fokker-Planck equation Markov chain Mathematics Science Stochastic Stochastic processes Tools algorithms stochastic process

Authors and affiliations

  • Alexandre Chorin
    • 1
  • Ole H. Hald
    • 2
  1. 1.Dept. MathematicsUniversity of California, BerkeleyBerkeleyU.S.A.
  2. 2.Dept. MathematicsUniversity of California, BerkeleyBerkeleyU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-1002-8
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-1001-1
  • Online ISBN 978-1-4419-1002-8
  • About this book