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Cover Art
Author Bouleau, Nicolas.

Title Numerical methods for stochastic processes / by Nicolas Bouleau, Dominique Lépingle.

Published New York : Wiley, [1994]


Location Call No. Status
Physical description xvii, 359 pages ; 25 cm.
Series Wiley series in probability and mathematical statistics. Applied probability and statistics.
Wiley series in probability and mathematical statistics. Applied probability and statistics.
Notes "A Wiley-Interscience publication."
Bibliography Includes bibliographical references (pages 337-351) and index.
Contents 1. Preliminaries. A. Set Theory and General Topology. B. Probability Theory. C. Random Processes. D. Wiener-Levy Calculus -- 2. Computation of Expectations in Finite Dimension. A. Mathematical Framework of Simulation. B. The Monte Carlo Method. C. Low-Discrepancy Sequences. D. Numerical Computation of Conditional Expectation -- 3. Simulation of Random Processes. A. Integration in Large or Infinite Dimensions. B. Representations of Stationary Fields. C. Markov Processes. D. Processes with Stationary Independent Increments. E. Point Processes -- 4. Deterministic Resolution of Some Markovian Problems. A. Elements in Markovian Potential Theory. B. Balayage Algorithms. C. Reduced Function Algorithm. D. The Carre du Champ Operator -- 5. Stochastic Differential Equations and Brownian Functionals. A. Lipschitzian Stochastic Differential Equations: Ito's Theorem. B. Discretization of SDEs. C. Irregularity of Brownian Functionals. D. Simulatable Functionals.
E. Symbolic Expansions of Solutions to SDEs. F. Application of the Shift Method to Multiple Wiener Integrals and to Solutions of SDEs.
Summary In recent years, random variables and stochastic processes have emerged as important factors in predicting outcomes in virtually every field of applied and social science. Ironically, according to Nicolas Bouleau and Dominique Lepingle, the presence of randomness in the model sometimes leads engineers to accept crude mathematical treatments that produce inaccurate results. The purpose of Numerical Methods for Stochastic Processes is to add greater rigor to numerical treatment of stochastic processes so that they produce results that can be relied upon when making decisions and assessing risks. Based on a postgraduate course given by the authors at Paris 6 University, the text emphasizes simulation methods, which can now be implemented with specialized computer programs. Specifically presented are the Monte Carlo and shift methods, which use an "imitation of randomness" and have a wide range of applications, and the so-called quasi-Monte Carlo methods, which are rigorous but less widely applicable. Offering a broad introduction to the field, this book presents the current state of the main methods and ideas and the cases for which they have been proved. Nevertheless, the authors do explore problems raised by these newer methods and suggest areas in which further research is needed. Extensive notes and a full bibliography give interested readers the option of delving deeper into stochastic numerical analysis. For professional statisticians, engineers, and physical and social scientists, Numerical Methods for Stochastic Processes provides both the theoretical background and the necessary practical tools to improve predictions based on randomness in the model. With its exercises andbroad-spectrum coverage, it is also an excellent textbook for introductory graduate-level courses in stochastic process mathematics.
Other author Lépingle, Dominique.
Subject Stochastic processes -- Mathematical models.
Monte Carlo method.
ISBN 0471546410 (acid-free)