Introduction to Monte-Carlo Methods for Transport and Diffusion Equations

Author: Bernard Lapeyre, Etienne Pardoux, Remi Sentis, Alan Craig and Fionn Craig Series: Oxford Texts in Applied and Engineering Mathematics

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1. Monte-Carlo methods and Integration 2. Transport equations and processes 3. The Monte-Carlo method for the transport equations 4. The Monte-Carlo method for the Boltzmann equation 5. The Monte-Carlo method for diffusion equations Bibliography Index

This text is aimed at graduate students in mathematics, physics, engineering, economics, finance, and the biosciences that are interested in using Monte-Carlo methods for the resolution of real-life scenarios.

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Summary

Monte-Carlo methods and Integration 2. Transport equations and processes 3. The Monte-Carlo method for the transport equations 4. The Monte-Carlo method for the Boltzmann equation 5. The Monte-Carlo method for diffusion equations Bibliography Index

Description

Monte-Carlo methods is the generic term given to numerical methods that use sampling of random numbers. This text is aimed at graduate students in mathematics, physics, engineering, economics, finance, and the biosciences that are interested in using Monte-Carlo methods for the resolution of partial differential equations, transport equations, the Boltzmann equation and the parabolic equations of diffusion. It includes applied examples, particularly in mathematicalfinance, along with discussion of the limits of the methods and description of specific techniques used in practice for each example.This is the sixth volume in the Oxford Textsin Applied and Engineering Mathematics series, which includes texts based on taught courses that explain the mathematical or computational techniques required for the resolution of fundamental applied problems, from the undergraduate through to the graduate level. Other books in the series include: Jordan & Smith: Nonlinear Ordinary Differential Equations: An introduction to Dynamical Systems; Sobey: Introduction to Interactive Boundary Layer Theory; Scott: Nonlinear Science: Emergenceand Dynamics of Coherent Structures; Tayler: Mathematical Models in Applied Mechanics; Ram-Mohan: Finite Element and Boundary Element Applications in Quantum Mechanics; Elishakoff and Ren: Finite ElementMethods for Structures with Large Stochastic Variations.

About the Author

Bernard Lapeyre is at Ecole Nationale des Ponts et Chaussees, Marne-la-Vallee, France. Etienne Pardoux is at Universite de Provence, Marseille, France. Remi Sentis is Commissariat a l'Energie Atomique Bruyeres-le-Chatel, France.

More on this Book

Monte-Carlo methods is the generic term given to numerical methods that use sampling of random numbers. This text is aimed at graduate students in mathematics, physics, engineering, economics, finance, and the biosciences that are interested in using Monte-Carlo methods for the resolution of partial differential equations, transport equations, the Boltzmann equation and the parabolic equations of diffusion. It includes applied examples, particularly in mathematical finance, along with discussion of the limits of the methods and description of specific techniques used in practice for each example.This is the sixth volume in the Oxford Texts in Applied and Engineering Mathematics series, which includes texts based on taught courses that explain the mathematical or computational techniques required for the resolution of fundamental applied problems, from the undergraduate through to the graduate level. Other books in the series include: Jordan & Smith: Nonlinear Ordinary Differential Equations: An introduction to Dynamical Systems; Sobey: Introduction to Interactive Boundary Layer Theory; Scott: Nonlinear Science: Emergence and Dynamics of Coherent Structures; Tayler: Mathematical Models in Applied Mechanics; Ram-Mohan: Finite Element and Boundary Element Applications in Quantum Mechanics; Elishakoff and Ren: Finite Element Methods for Structures with Large Stochastic Variations.