A second-order Monte Carlo method for the solution of the Ito stochastic differential equation |
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Authors: | DC Haworth SB Pope |
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Institution: | Sibley School of Mechanical and Aerospace Engineering , Cornell University , Ithaca, New York, 14853 |
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Abstract: | A difference approximation that is second-order accurate in the time step his derived for the general Ito stochastic differential equation. The difference equation has the form of a second-order random walk in which the random terms are non-linear combinations of Gaussian random variables. For a wide class of problems, the transition pdf is joint-normal to second order in h; the technique then reduces to a Gaussian random walk, but its application is not limited to problems having a Gaussian solution. A large number of independent sample paths are generated in a Monte Carlo solution algorithm; any statistical function of the solution (e.g., moments or pdf's) can be estimated by ensemble averaging over these paths |
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