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Consistency of stochastic approximation algorithm with quasi-associated random errors

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  • Idir Arab
  • Abdelnasser Dahmani

Abstract

Many mathematical and physical problems are led to find a root of a real function f. This kind of equation is an inverse problem and it is difficult to solve it. Especially in engineering sciences, the analytical expression of the function f is unknown to the experimenter, but it can be measured at each point xk with M(xk) as expected value and induced error ξk. The aim is to approximate the unique root θ under some assumptions on the function f and errors ξk. We use a stochastic approximation algorithm that constructs a sequence (xk)k ⩾ 1. We establish the almost complete convergence of the sequence (xk)k to the exact root θ by considering the errors (ξk)k quasi-associated and we illustrate the method by numerical examples to show its efficiency.

Suggested Citation

  • Idir Arab & Abdelnasser Dahmani, 2016. "Consistency of stochastic approximation algorithm with quasi-associated random errors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(23), pages 6883-6890, December.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:23:p:6883-6890
    DOI: 10.1080/03610926.2014.968737
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