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Martingale Limit Theory and Its Application
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The article was published on 2014-09-23 and is currently open access. It has received 3075 citations till now. The article focuses on the topics: Local martingale & Doob's martingale inequality.read more
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On-board Component Fault Detection and Isolation Using the Statistical Local Approach
TL;DR: Both the key principles and real application examples of a unified theory which allows us to perform the on-board incipient fault detection and isolation tasks involved in monitoring for condition-based maintenance are described.
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Central limit theorems for additive functionals of Markov chains
TL;DR: In this article, central limit theorems and invariance principles are obtained for additive functionals of a stationary ergodic Markov chain, where the conditions imposed restrict the moments of $g$ and the growth of the conditional means.
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The foundations of finite sample estimation in stochastic processes
TL;DR: In this paper, a finite sample optimal estimation of a discrete stochastic process is established for samples of finite size n, where n is the number of samples in the process.
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Accuracy analysis for wavelet approximations
TL;DR: Unlike neural network training, this estimation procedure does not rely on stochastic gradient type techniques such as the celebrated "backpropagation" and it completely avoids the problem of poor convergence or undesirable local minima.
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Local Whittle estimation in nonstationary and unit root cases
TL;DR: In this article, the local Whittle estimator in the nonstationary case (d> 1 ) was investigated and it was shown that the estimator converges in probability to unity with a polynomial trend of order α > 1.