## Abstract

A difference approximation that is second-order accurate in the time step h is 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.

Original language | English (US) |
---|---|

Pages (from-to) | 151-186 |

Number of pages | 36 |

Journal | Stochastic Analysis and Applications |

Volume | 4 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1986 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics