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

Released on by Nawaf Bou-Rabee
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  • Continuous-Time Random Walks for the Numerical Solution of Stochastic Differential Equations Book Detail

  • Author : Nawaf Bou-Rabee
  • Release Date : 2019-01-08
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 136
  • ISBN 13 : 1470431815
  • File Size : 21,21 MB
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Continuous-Time Random Walks for the Numerical Solution of Stochastic Differential Equations by Nawaf Bou-Rabee PDF Summary

Book Description: 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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