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Simulation

  • Paolo Baldi
Chapter
Part of the Universitext book series (UTX)

Abstract

Applications often require the computation of the expectation of a functional of a diffusion process. But for a few situations there is no closed formula in order to do this and one must recourse to approximations and numerical methods. We have seen in the previous chapter that sometimes such an expectation can be obtained by solving a PDE problem so that specific numerical methods for PDEs, such as finite elements, can be employed. Simulation of diffusion processes is another option which is explored in this chapter.

References

  1. Gilbarg, D. and Trudinger, N. S. (2001). Elliptic partial differential equations of second order. Classics in Mathematics. Springer-Verlag, Berlin. Reprint of the 1998 edition.Google Scholar
  2. Graham, C. and Talay, D. (2013). Stochastic simulation and Monte Carlo methods, volume 68 of Stochastic Modelling and Applied Probability. Springer, Heidelberg. Mathematical foundations of stochastic simulation.CrossRefzbMATHGoogle Scholar
  3. Maruyama, G. (1955). Continuous Markov processes and stochastic equations. Rend. Circ. Mat. Palermo (2), 4:48–90.CrossRefzbMATHMathSciNetGoogle Scholar
  4. Talay, D. and Tubaro, L. (1990). Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Anal. Appl., 8(4):483–509 (1990).Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Paolo Baldi
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly

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