Numerical simulation of a linear stochastic oscillator with additive noise

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Strømmen Melbø, A.H. and Higham, D.J. (2004) Numerical simulation of a linear stochastic oscillator with additive noise. Applied Numerical Mathematics, 51 (1). pp. 89-99. ISSN 0168-9274 (https://doi.org/10.1016/j.apnum.2004.02.003)

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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.

ORCID iDs

Strømmen Melbø, A.H. and Higham, D.J. ORCID logoORCID: https://orcid.org/0000-0002-6635-3461;
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