Discrete-time Approximations of Stochastic Delay Equations: the Milstein Scheme By
نویسندگان
چکیده
In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDEs). The scheme has convergence order 1. In order to establish the scheme, we prove an infinitedimensional Itô formula for “tame” functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use of the Malliavin calculus and the anticipating stochastic analysis of Nualart and Pardoux. Given the nonanticipating nature of the SDDE, the use of anticipating calculus methods in the context of strong approximation schemes appears to be novel.
منابع مشابه
The Milstein Scheme for Stochastic Delay Differential Equations without Anticipative Calculus
The Milstein scheme is the simplest nontrivial numerical scheme for stochastic differential equations with a strong order of convergence one. The scheme has been extended to the stochastic delay differential equations but the analysis of the convergence is technically complicated due to anticipative integrals in the remainder terms. This paper employs an elementary method to derive the Milstein...
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