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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 1 open journal systems 


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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Pages: 1-9

Published on: January 2, 2008


Bibliography
  1. Bykov, A. A. Numerical solution of stiff Cauchy problems for systems of linear ordinary differential equations.(Russian) Vychisl. Metody i Programmirovanie No. 38 (1983), 173--181. MR0734303 (85b:65059)
  2. Fierro, Raúl; Torres, Soledad. The Euler scheme for Hilbert space valued stochastic differential equations. Statist. Probab. Lett. 51 (2001), no. 3, 207--213. MR1822727 (2001m:65018)
  3. Henrici, Peter. Discrete variable methods in ordinary differential equations.John Wiley & Sons, Inc., New York-London 1962 xi+407 pp. MR0135729 (24 #B1772)
  4. Kloeden, Peter E.; Platen, Eckhard. Numerical solution of stochastic differential equations.Applications of Mathematics (New York), 23. Springer-Verlag, Berlin, 1992. xxxvi+632 pp. ISBN: 3-540-54062-8 MR1214374 (94b:60069)
  5. Rebolledo, Rolando. Central limit theorems for local martingales. Z. Wahrsch. Verw. Gebiete 51 (1980), no. 3, 269--286. MR0566321 (81g:60023)
  6. San Martín, Jaime; Torres, Soledad. Euler scheme for solutions of a countable system of stochastic differential equations. Statist. Probab. Lett. 54 (2001), no. 3, 251--259. MR1857939 (2002h:65007)
  7. Srinivasu, P. D. N.; Venkatesulu, M. Quadratically convergent numerical schemes for nonstandard initial value problems. Appl. Math. Comput. 47 (1992), no. 2-3, 145--154. MR1143148 (92m:65089b)
  8. Wollman, Stephen. Convergence of a numerical approximation to the one-dimensional Vlasov-Poisson system. Transport Theory Statist. Phys. 19 (1990), no. 6, 545--562. MR1090947 (92c:82107)
















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Electronic Communications in Probability. ISSN: 1083-589X