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April 2015 A decreasing step method for strongly oscillating stochastic models
Camilo Andrés García Trillos
Ann. Appl. Probab. 25(2): 986-1029 (April 2015). DOI: 10.1214/14-AAP1016

Abstract

We propose an algorithm for approximating the solution of a strongly oscillating SDE, that is, a system in which some ergodic state variables evolve quickly with respect to the other variables. The algorithm profits from homogenization results and consists of an Euler scheme for the slow scale variables coupled with a decreasing step estimator for the ergodic averages of the quick variables. We prove the strong convergence of the algorithm as well as a C.L.T. like limit result for the normalized error distribution. In addition, we propose an extrapolated version that has an asymptotically lower complexity and satisfies the same properties as the original version.

Citation

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Camilo Andrés García Trillos. "A decreasing step method for strongly oscillating stochastic models." Ann. Appl. Probab. 25 (2) 986 - 1029, April 2015. https://doi.org/10.1214/14-AAP1016

Information

Published: April 2015
First available in Project Euclid: 19 February 2015

zbMATH: 1316.60111
MathSciNet: MR3313761
Digital Object Identifier: 10.1214/14-AAP1016

Subjects:
Primary: 60H35
Secondary: 65C30

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 2 • April 2015
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