Abstract
A method for the numerical solution of stochastic differential equations is presented. The method has mean-square order equal to 1/2 when it is applied to a general stochastic differential equation and equal to 1 if the equation has additive noise. In addition, it is shown that the method captures some long-time properties of a linear stochastic oscillator: It reproduces exactly the growth rate of the second moment and the oscillation property of the solution.
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AMS subject classification (2000)
60H10, 34F05, 65U05, 60K40
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TOCINO, A. On preserving long-time features of a linear stochastic oscillator . Bit Numer Math 47, 189–196 (2007). https://doi.org/10.1007/s10543-007-0115-2
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DOI: https://doi.org/10.1007/s10543-007-0115-2