## Journal of Applied Mathematics

### Exact Finite-Difference Schemes for $d$-Dimensional Linear Stochastic Systems with Constant Coefficients

#### Abstract

The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 830936, 6 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808246

Digital Object Identifier
doi:10.1155/2013/830936

Mathematical Reviews number (MathSciNet)
MR3138940

Zentralblatt MATH identifier
06950895

#### Citation

Jiang, Peng; Ju, Xiaofeng; Liu, Dan; Fan, Shaoqun. Exact Finite-Difference Schemes for $d$ -Dimensional Linear Stochastic Systems with Constant Coefficients. J. Appl. Math. 2013 (2013), Article ID 830936, 6 pages. doi:10.1155/2013/830936. https://projecteuclid.org/euclid.jam/1394808246

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