Numerical Methods and Stochastics

T. J. Lyons · Thomas Stephenson Salisbury

Fields Institute Communications 34 巻 · American Mathematical Soc.

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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 discussparticle 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 fastdynamo 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.