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Numerical Methods and Stochastics
Edited by: T. J. Lyons, University of Oxford, UK, and T. S. Salisbury, York University, Toronto, ON, Canada
A co-publication of the AMS and Fields Institute.
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Fields Institute Communications
2002; 121 pp; hardcover
Volume: 34
ISBN-10: 0-8218-1994-1
ISBN-13: 978-0-8218-1994-4
List Price: US$57
Member Price: US$45.60
Order Code: FIC/34
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This volume represents the proceedings of the Workshop on Numerical Methods and Stochastics held at The Fields Institute in April 1999. The goal of the workshop was to identify emerging ideas in probability theory that influence future work in both probability and numerical computation. The book focuses on new results and gives novel approaches to computational problems based on the latest techniques from the theory of probability and stochastic processes.

Three papers discuss particle system approximations to solutions of the stochastic filtering problem. Two papers treat particle system equations. The paper on "rough paths" describes how to generate good approximations to stochastic integrals. An expository paper discusses a long-standing conjecture: the stochastic fast dynamo effect. A final paper gives an analysis of the error in binomial and trinomial approximations to solutions of the Black-Scholes stochastic differential equations.

The book is intended for graduate students and research mathematicians interested in probability theory.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students and advanced research mathematicians interested in probability theory.

Reviews

"Eight studies explore novel approaches to computational problems using recent technology from the theory of probability and stochastic processes. Rather than emphasizing a single set of techniques, they describe both particle systems approaches and stochastic analysis."

-- Book News, Inc.

Table of Contents

  • D. Crisan -- Numerical methods for solving the stochastic filtering problem
  • D. Crisan and T. Lyons -- Optimal filtering on discrete sets
  • P. Del Moral and J. Jacod -- The Monte-Carlo method for filtering with discrete-time observations: Central limit theorems
  • A. Guionnet -- Approximations of Markovian non linear partial differential equations by particle systems
  • A. Guionnet -- Non-Markovian limit diffusions and spin glasses
  • S. B. Hazra and F. G. Viens -- Towards pathwise stochastic fast dynamo in magneto-hydrodynamics
  • T. J. Lyons -- System control and rough paths
  • J. B. Walsh and O. D. Walsh -- Embedding and the convergence of the binomial and trinomial tree schemes
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