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 and in the sense respectively, where 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

Email:
shoji@shako.sk.tsukuba.ac.jp

DOI:
https://doi.org/10.1090/S0025-5718-98-00888-6

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