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2006.2: The Weak Euler Scheme for Stochastic Differential Delay Equations

2006.2: Evelyn Buckwar, Rachel Kuske, Salah-Eldin Mohammed and Tony Shardlow (2006) The Weak Euler Scheme for Stochastic Differential Delay Equations.

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Abstract

We develop a weak numerical Euler scheme for non-linear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The weak Euler scheme has order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay).The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.

Item Type:MIMS Preprint
Subjects:MSC 2000 > 39 Difference and functional equations
MSC 2000 > 60 Probability theory and stochastic processes
MSC 2000 > 65 Numerical analysis
MIMS number:2006.2
Deposited By:Tony Shardlow
Deposited On:05 January 2006

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