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Spurious oscillation in a uniform Euler discretisation of linear stochastic differential equations with vanishing delay. (English) Zbl 1122.65011

The oscillatory behaviour of the solutions to linear stochastic differential equations with vanishing delay has been investigated by the authors in a previous paper [Funct. Differ. Equ. 11, 235–265 (2004; Zbl 1064.34068)]. Here they construct a discrete model that successfully mimics some of the properties of the continuous process. However, care must be taken: uniform mesh yields spurious oscillatory behaviour.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
34K50 Stochastic functional-differential equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

Citations:

Zbl 1064.34068

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References:

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[2] Appleby, J. A.D.; Kelly, C., Asymptotic and oscillatory properties of linear stochastic delay differential equations with vanishing delay, Funct. Differential Equation, 11, 3-4, 235-265 (2004) · Zbl 1064.34068
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