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Continuous-Time Random Walks for the Numerical Solution of Stochastic Differential Equations

Nawaf Bou-Rabee Rutgers University Camden, NJ
Eric Vanden-Eijnden Courant Institute of Mathematical Sciences, New York University, NY
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Softcover ISBN: 978-1-4704-3181-5
Product Code: MEMO/256/1228
List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $46.80 Electronic ISBN: 978-1-4704-4919-3 Product Code: MEMO/256/1228.E List Price:$78.00
MAA Member Price: $70.20 AMS Member Price:$46.80
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AMS Member Price: $70.20 Click above image for expanded view Continuous-Time Random Walks for the Numerical Solution of Stochastic Differential Equations Nawaf Bou-Rabee Rutgers University Camden, NJ Eric Vanden-Eijnden Courant Institute of Mathematical Sciences, New York University, NY Available Formats:  Softcover ISBN: 978-1-4704-3181-5 Product Code: MEMO/256/1228  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$46.80
 Electronic ISBN: 978-1-4704-4919-3 Product Code: MEMO/256/1228.E
 List Price: $78.00 MAA Member Price:$70.20 AMS Member Price: $46.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$117.00 MAA Member Price: $105.30 AMS Member Price:$70.20
• Book Details

Memoirs of the American Mathematical Society
Volume: 2562018; 124 pp
MSC: Primary 65; Secondary 60;

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.

• Chapters
• 1. Introduction
• 2. Algorithms
• 3. Examples & Applications
• 4. Analysis on Gridded State Spaces
• 5. Analysis on Gridless State Spaces
• 6. Tridiagonal Case
• 7. Conclusion and Outlook

• Requests

Review Copy – for reviewers who would like to review an AMS book
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Volume: 2562018; 124 pp
MSC: Primary 65; Secondary 60;

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.

• Chapters
• 1. Introduction
• 2. Algorithms
• 3. Examples & Applications
• 4. Analysis on Gridded State Spaces
• 5. Analysis on Gridless State Spaces
• 6. Tridiagonal Case
• 7. Conclusion and Outlook
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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