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Approximation of continuous time stochastic processes by a local linearization method

Author: Isao Shoji
Journal: Math. Comp. 67 (1998), 287-298
MSC (1991): Primary 65D30, 65B33; Secondary 60H10
MathSciNet review: 1432134
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Abstract: This paper investigates the rate of convergence of an alternative approximation method for stochastic differential equations. The rates of convergence of the one-step and multi-step approximation errors are proved to be $O((\Delta t)^2) $ and $O(\Delta t)$ in the $L_p$ sense respectively, where $\Delta t$ is discrete time interval. The rate of convergence of the one-step approximation error is improved as compared with methods assuming the value of Brownian motion to be known only at discrete time. Through numerical experiments, the rate of convergence of the multi-step approximation error is seen to be much faster than in the conventional method.

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Additional Information

Isao Shoji
Affiliation: Institute of Policy and Planning Sciences, University of Tsukuba, Tsukuba Ibaraki 305, Japan

Keywords: Stochastic differential equations, discretization, rate of convergence, numerical approximation
Received by editor(s): May 19, 1996
Received by editor(s) in revised form: September 4, 1996
Article copyright: © Copyright 1998 American Mathematical Society

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