# American Institute of Mathematical Sciences

May  2013, 18(3): 667-679. doi: 10.3934/dcdsb.2013.18.667

## The spectral collocation method for stochastic differential equations

 1 Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States 2 Department of Mathematics, Wayne State University, Detroit, MI 48202, United States

Received  January 2012 Revised  September 2012 Published  December 2012

In this paper, we use the Chebyshev spectral collocation method to solve a certain type of stochastic differential equations (SDEs). We also use this method to estimate parameters of stochastic differential equations from discrete observations by maximum likelihood technique and Kessler technique. Our numerical tests shows that the spectral method gives better results than the Euler's method and the Shoji-Ozaki method.
Citation: Can Huang, Zhimin Zhang. The spectral collocation method for stochastic differential equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (3) : 667-679. doi: 10.3934/dcdsb.2013.18.667
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##### References:
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