Mao, X. and Yuan, C. (2008) *A note on the rate of convergence of the Euler-Maruyama method for stochastic differential equations.* Stochastic Analysis and Applications, 26 (2). pp. 325-333. ISSN 0736-2994

## Abstract

The recent article [2] reveals the strong convergence of the Euler-Maruyama solution to the exact solution of a stochastic differential equation under the local Lipschitz condition. However, it does not provide us with an order of convergence. In this note, we will show the rate of convergence still under the local Lipschitz condition, but the local Lipschitz constants of the drift coefficient, valid on balls of radius R, are supposed not to grow faster than log R while those of the diffusion coefficient are not than.

Item type: | Article |
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ID code: | 14042 |

Keywords: | brownian motion, euler-maruyama method, lipschitz condition, differential equations, Mathematics, Applied Mathematics, Statistics and Probability, Statistics, Probability and Uncertainty |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Mrs Carolynne Westwood |

Date Deposited: | 11 Jan 2010 16:59 |

Last modified: | 04 Sep 2014 22:22 |

URI: | http://strathprints.strath.ac.uk/id/eprint/14042 |

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