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Invariance principles for standard-normalized and self-normalized random fields
Functional central limit theorem invariance principle i.i.d. random elds martingale-dierence random elds Orlicz spaces metric entropy self-normalization
2009/6/12
We investigate the invariance principle for set-indexed partial sums of a stationary field (X ) d of martingale-di?erence or independent random variables kk-Z under standard normalization or self-norm...
Recent advances in invariance principles for stationary sequences
Brownian motion weakly dependent sequences martingale differences linear process central limit theorem invariance principle
2009/5/18
In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main too...
Invariance Principles for Ranked Excursion Lengths and Heights
excursion lengths excursion heights invariance principle
2009/4/28
In this note we prove strong invariance principles between ranked excursion lengths and heights of a simple random walk and those of a standard Brownian motion. Some consequences concerning limiting d...
Invariance principles for linear processes Application to isotonic regression
linear processes moment inequalities generalizations of martingales invariance principles fractional Brownian motion isotonic regression
2010/3/18
In this paper we prove maximal inequalities and study the functional central
limit theorem for the partial sums of linear processes generated by dependent
innovations. Due to the general weights the...