Introduction to Monte Carlo Methods for Transport and Diffusion - Equation

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.

Sommario

• 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

Riassunto

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.

Dettagli sul prodotto

• Autori: Bernard Lapeyre, Bernard ( Lapeyre, Bernard (Ecole Nationale Des Ponts Et Cha Lapeyre, Bernard Pardoux Lapeyre, Lapeyre Bernard, Etienne Pardoux, Pardoux Etienne, Remi Sentis, Sentis Remi
• Con la collaborazione di: Alan Craig (Traduzione), Fionn Craig (Traduzione), Craig Alan (Traduzione), Craig Fionn (Traduzione)
• Editore: Oxford University Press
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 24.07.2003
• EAN: 9780198525936
• ISBN: 978-0-19-852593-6
• Pagine: 174
• Serie: Oxford Texts in Applied and Engineering Mathematics; Mathematics; Oxford Texts in Applied and Engineering Mathematics
• Categorie: Scienze naturali, medicina, informatica, tecnica > Matematica; MATHEMATICS / Probability & Statistics / General, MATHEMATICS / Applied, MATHEMATICS / Mathematical Analysis, Probability & statistics, Calculus & mathematical analysis, Maths for scientists, Maths for engineers, Probability and statistics, Calculus and mathematical analysis