The Weak Euler Scheme for Stochastic Differential Delay Equations

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

PDF weak_mal_web.pdf Download (331kB)

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 2010, the AMS's Mathematics Subject Classification > 39 Difference and functional equations MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Tony Shardlow
Date Deposited:	05 Jan 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/136

Available Versions of this Item

• The Weak Euler Scheme for Stochastic Differential Delay Equations. (deposited 05 Jan 2006) [Currently Displayed]
  • The Weak Euler Scheme for Stochastic Differential Delay Equations. (deposited 24 Jan 2006)

Actions (login required)

View Item