Weak approximation of stochastic differential delay equations

Evelyn Buckwar and Tony Shardlow

No 2001,88, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

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.

Keywords: Stochastic delay equations; Theoretical approximation of solutions; Stochastic partial differential equations; Stability and convergence of numerical approximations (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb373:200188

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