Electronic Communications in Probability

A stochastic scheme of approximation for ordinary differential equations

Raul Fierro and Soledad Torres

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Abstract

In this note we provide a stochastic method for approximating solutions of ordinary differential equations. To this end, a stochastic variant of the Euler scheme is given by means of Markov chains. For an ordinary differential equation, these approximations are shown to satisfy a Large Number Law, and a Central Limit Theorem for the corresponding fluctuations about the solution of the differential equation is proven.

Article information

Source
Electron. Commun. Probab., Volume 13 (2008), paper no. 1, 1-9.

Dates
Accepted: 21 November 2007
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465233428

Digital Object Identifier
doi:10.1214/ECP.v13-1341

Mathematical Reviews number (MathSciNet)
MR2372832

Zentralblatt MATH identifier
1190.60058

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Numerical Scheme Convergence in law Central limit theorem

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Fierro, Raul; Torres, Soledad. A stochastic scheme of approximation for ordinary differential equations. Electron. Commun. Probab. 13 (2008), paper no. 1, 1--9. doi:10.1214/ECP.v13-1341. https://projecteuclid.org/euclid.ecp/1465233428


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References

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