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2008 A stochastic scheme of approximation for ordinary differential equations
Raul Fierro, Soledad Torres
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Electron. Commun. Probab. 13: 1-9 (2008). DOI: 10.1214/ECP.v13-1341


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.


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Raul Fierro. Soledad Torres. "A stochastic scheme of approximation for ordinary differential equations." Electron. Commun. Probab. 13 1 - 9, 2008.


Accepted: 21 November 2007; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1190.60058
MathSciNet: MR2372832
Digital Object Identifier: 10.1214/ECP.v13-1341

Primary: 60H10

Keywords: central limit theorem , convergence in law , Numerical scheme

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