Numerical simulation of a linear stochastic oscillator with additive noise

Authors:
Aslaug H. Strømmen Melbø;Desmond J. Higham
Affiliations:
WesternGeco Oslo Technology Center, P.O. Box 234, 1372 Asker, Norway and Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway;Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, UK
Venue:
Applied Numerical Mathematics
Year:
2004

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Original articles: On the numerical discretisation of stochastic oscillators

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Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise

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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.