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A stochastic scheme of approximation for ordinary differential equations. (English) Zbl 1190.60058

Summary: 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.

MSC:

60J05 Discrete-time Markov processes on general state spaces
34F05 Ordinary differential equations and systems with randomness
65C20 Probabilistic models, generic numerical methods in probability and statistics
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