Probability and Partial Differential Equations in Modern Applied Mathematics

  • Edward C. Waymire
  • Jinqiao Duan
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 140)

Table of contents

  1. Front Matter
    Pages i-x
  2. Rabi Bhattacharya, Larry Chen, Ronald B. Guenther, Crris Orum, Mina Ossiander, Enrique Thomannii et al.
    Pages 27-40
  3. Vena Pearl Boncolan-Walsh, Jinqiao Duan, Hongjun Gao, Tamay Özgökmen, Paul Fischer, Traian Iliescu
    Pages 61-77
  4. Ian M. Davies, Aubrey Truman, Huaizhong Zhao
    Pages 79-95
  5. William G. Faris
    Pages 97-115
  6. Martin Greiner, Jochen Cleve, Jürgen Schmiege, Katepalli R. Sreenivasan
    Pages 137-150
  7. Yves Le Jaw, Olivier Raimond
    Pages 151-162
  8. Mukul Majumdar
    Pages 181-195
  9. Back Matter
    Pages 259-262

About this book

Introduction

"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.

Keywords

Markov Markov chain Stochas Stochastic calculus calculus differential equation dynamical systems dynamische Systeme ergodicity mathematical modeling modeling numerical analysis partial differential equation random dynamical system rough path

Editors and affiliations

  • Edward C. Waymire
    • 1
  • Jinqiao Duan
    • 2
  1. 1.Department of MathematicsOregon State UniversityCovallis
  2. 2.Department of Applied MathematicsIllionis Institute of TechnologyChicago

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-29371-4
  • Copyright Information Springer-Verlag New York 2005
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-25879-9
  • Online ISBN 978-0-387-29371-4
  • Series Print ISSN 0940-6573
  • About this book