**Fields Institute Communications**

Volume: 34;
2002;
121 pp;
Hardcover

MSC: Primary 60;
Secondary 65

Print ISBN: 978-0-8218-1994-4

Product Code: FIC/34

List Price: $60.00

Individual Member Price: $48.00

**Electronic ISBN: 978-1-4704-3068-9
Product Code: FIC/34.E**

List Price: $60.00

Individual Member Price: $48.00

# Numerical Methods and Stochastics

Share this page *Edited by *
*T. J. Lyons; T. S. Salisbury*

A co-publication of the AMS and Fields Institute

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 & Endorsements

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

## Numerical Methods and Stochastics

- Cover Cover11
- Title page i2
- Contents iii4
- Preface v6
- Numerical methods for solving the stochastic filtering problem 18
- Optimal filtering on discrete sets 2128
- The Monte-Carlo method for filtering with discrete-time observations: Central limit theorems 2936
- Approximations of Markovian non linear partial differential equations by particle systems 5562
- Non-Markovian limit diffusions and spin glasses 6572
- Towards pathwise stochastic fast dynamo in magneto-hydrodynamics 7582
- System control and rough paths 9198
- Embedding and the convergence of the binomial and trinomial tree schemes 101108
- Back Cover Back Cover1129