Continuous-Time Random Walks for the Numerical Solution of Stochastic Differential Equations: November 2018 (Memoirs of the American Mathematical Society)

Bou-rabee, Nawaf, Vanden-eijnden, Eric

ISBN 10: 1470431815 / ISBN 13: 9781470431815

Published by Amer Mathematical Society, 2018

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Bibliographic Details

• Title: Continuous-Time Random Walks for the Numerical Solution of Stochastic Differential Equations: November 2018 (Memoirs of the American Mathematical Society)
• Publisher: Amer Mathematical Society
• Publication Date: 2018
• Language: English
• ISBN 10: 1470431815
• ISBN 13: 9781470431815
• Binding: paperback
• Condition: New
• Book Type: book

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Synopsis

This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These schemes are obtained by spatially discretizing the Kolmogorov equation associated with the SDE in such a way that the resulting semi-discrete equation generates a Markov jump process that can be realized exactly using a Monte Carlo method. In this construction the jump size of the approximation can be bounded uniformly in space, which often guarantees that the schemes are numerically stable for both finite and long time simulation of SDEs.