Numerical simulation of a linear stochastic oscillator with additive noise

A.H. Strømmen Melbø; D.J. Higham

doi:10.1016/j.apnum.2004.02.003

Numerical simulation of a linear stochastic oscillator with additive noise

A.H. Strømmen Melbø, D.J. Higham

Mathematics And Statistics

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Abstract

The ability of numerical methods to reproduce long-time features of a linear stochastic oscillator is examined. It is shown that certain, widely-used, methods fail to capture the correct second moment growth rate, whereas a customized extension of the partitioned Euler method behaves well in this respect. It is also shown that the partitioned Euler method inherits an infinite-oscillation property. A weaker oscillation result is proved for a wide class of numerical methods.

Original language	English
Pages (from-to)	89-99
Number of pages	10
Journal	Applied Numerical Mathematics
Volume	51
Issue number	1
DOIs	https://doi.org/10.1016/j.apnum.2004.02.003
Publication status	Published - Oct 2004

Keywords

numerical methods
mathematics
linear stochastic oscillator
Euler method

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10.1016/j.apnum.2004.02.003

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title = "Numerical simulation of a linear stochastic oscillator with additive noise",

abstract = "The ability of numerical methods to reproduce long-time features of a linear stochastic oscillator is examined. It is shown that certain, widely-used, methods fail to capture the correct second moment growth rate, whereas a customized extension of the partitioned Euler method behaves well in this respect. It is also shown that the partitioned Euler method inherits an infinite-oscillation property. A weaker oscillation result is proved for a wide class of numerical methods.",

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AB - The ability of numerical methods to reproduce long-time features of a linear stochastic oscillator is examined. It is shown that certain, widely-used, methods fail to capture the correct second moment growth rate, whereas a customized extension of the partitioned Euler method behaves well in this respect. It is also shown that the partitioned Euler method inherits an infinite-oscillation property. A weaker oscillation result is proved for a wide class of numerical methods.

KW - numerical methods

KW - mathematics

KW - linear stochastic oscillator

KW - Euler method

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DO - 10.1016/j.apnum.2004.02.003

M3 - Article

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JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

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Numerical simulation of a linear stochastic oscillator with additive noise

Abstract

Keywords

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