Uniform iterated logarithm laws for martingales and their application to functional estimation in controlled Markov chains

R. Senoussi

Stochastic Processes and their Applications, 2000, vol. 89, issue 2, 193-211

Abstract: In the first part, we establish an upper bound of an iterated logarithm law for a sequence of processes endowed with the uniform convergence on compacts, where Mn(x) is a square integrable martingale for each x in . In the second part we present an iterative kernel estimator of the driving function f of the regression model:Xn+1=f(Xn)+[var epsilon]n+1.Strong convergences and CLT results are proved for this estimator and then extended to controlled Markov models.

Keywords: Iterated; logarithm; law; Autoregressive; model; Controlled; model; Markov; chain; Kernel; estimator (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (2)

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