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

Nawaf Bou-Rabee, Eric Vanden-Eijnden (Autoren)

Buch | Softcover

124 Seiten

2019
American Mathematical Society (Verlag)
978-1-4704-3181-5 (ISBN)

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Introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids.

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.

Nawaf Bou-Rabee, Rutgers University Camden, NJ. Eric Vanden-Eijnden, Courant Institute of Mathematical Sciences, New York University, NY.

Introduction
Algorithms
Examples and applications
Analysis on gridded state spaces
Analysis on gridless state spaces
Tridiagonal case
Conclusion and outlook
Bibliography.

Erscheinungsdatum	31.10.2018
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	205 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	1-4704-3181-5 / 1470431815
ISBN-13	978-1-4704-3181-5 / 9781470431815
Zustand	Neuware