The IMA Volumes in Mathematics and its Applications

Probability and Partial Differential Equations in Modern Applied Mathematics

Editors: Waymire, Edward C. (Ed.)

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About this book

"Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations.

This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.

Table of contents (16 chapters)

  • Nonnegative Markov Chains with Applications

    Athreya, K. S.

    Pages 1-9

  • Phase Changes with Time and Multi-Scale Homogenizations of a Class of Anomalous Diffusions

    Bhattacharya, Rabi

    Pages 11-26

  • Semi-Markov Cascade Representations of Local Solutions to 3-D Incompressible Navier-Stokes

    Bhattacharya, Rabi (et al.)

    Pages 27-40

  • Amplitude Equations for Spdes: Approximate Centre Manifolds and Invariant Measures

    Blömker, Dirk (et al.)

    Pages 41-59

  • Enstrophy and Ergodicity Of Gravity Currents

    Boncolan-Walsh, Vena Pearl (et al.)

    Pages 61-77

Buy this book

eBook n/a
  • ISBN 978-0-387-29371-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-0-387-25879-9
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-1-4419-2071-3
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Probability and Partial Differential Equations in Modern Applied Mathematics
Editors
  • Edward C. Waymire
Series Title
The IMA Volumes in Mathematics and its Applications
Series Volume
140
Copyright
2005
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-29371-4
DOI
10.1007/978-0-387-29371-4
Hardcover ISBN
978-0-387-25879-9
Softcover ISBN
978-1-4419-2071-3
Series ISSN
0940-6573
Edition Number
1
Number of Pages
X, 272
Number of Illustrations and Tables
22 b/w illustrations
Topics