A stochastic scheme of approximation for ordinary differential
equations
Raul Fierro, Universidad Catolica de Valparaiso
Soledad Torres, Universidad de
Valparaiso
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.
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