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