A maximal _{}-inequality for stationary sequences and its applications
By Magda Peligrad, Sergey Utev, Wei Biao Wu. 2006
52 citations recorded by the source corpus.
The paper aims to establish a new sharp Burkholder-type maximal inequality in Lp for a class of stationary sequences that includes martingale sequences, mixingales and other dependent structures. The case when the variables are bounded is also addressed, leading to an exponential inequality for a maximum of partial sums. As an application we present an invariance principle for partial sums of certain maps of Bernoulli shifts processes.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/906a53758ee2f8023d05cd5da3f97518b3e9c5ec
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In Applied Mathematics
- Marta Tyran-Kamińska
- E. Rio
- Wei Biao Wu
- Xiaohui Chen
- Weidong Liu
- Clifford Lam
- Pedro C. L. Souza
- Xiaofeng Shao
In Mathematical Physics
- E. Rio
- Marta Tyran-Kamińska
- Wei Biao Wu
- Xiaofeng Shao
- F. Merlevède
- Richard A. Davis
- Magda Peligrad
- Heng Liu
Citations in the corpus
- Convergence to Lévy stable processes under some weak dependence conditions (2009, methodology): “e have E(| Xn j=1 Zj(a)|2) ≤ KnE(|Z1(a)|2). Using the multivariate version of the Doob’s inequality for martingales, we also have the extension of the maximal inequality for stationary sequences from [33] which, together with the estimate in [33, Lemma 1], gives existence of a constant K1 such that ”
- STRONG INVARIANCE PRINCIPLES FOR DEPENDENT RANDOM VARIABLES (2007, background): “Peligrad, Utev and Wu [ 41 ] proved the above inequality when q ≥ 2 [see inequality (10) therein], while Wu and Zhao [70] proved it under 1 < q < 2. Note that k E(S2j |F0)k q ≤ P 2”
- Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions (2009, methodology): “For p> 2, Peligrad, Utev and Wu [ 13 ] generalize the Marcinkiewicz-Zygmund inequality to stationary weakly dependent sequences.”