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Weak approximation of stochastic differential delay equations

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  • Buckwar, Evelyn
  • Shardlow, Tony

Abstract

A numerical method for a class of Itô stochastic differential equations with a finite delay term is introduced. The method is based on the forward Euler approximation and is parameterised by its time step. Weak convergence with respect to a class of smooth test functionals is established by using the infinite dimensional version of the Kolmogorov equation. With regularity assumptions on coefficients and initial data, the rate of convergence is shown to be proportional to the time step. Some computations are presented to demonstrate the rate of convergence.

Suggested Citation

  • Buckwar, Evelyn & Shardlow, Tony, 2001. "Weak approximation of stochastic differential delay equations," SFB 373 Discussion Papers 2001,88, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200188
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    References listed on IDEAS

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    1. Küchler, Uwe & Platen, Eckhard, 2000. "Strong discrete time approximation of stochastic differential equations with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 189-205.
    2. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
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