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A maximal  -inequality for stationary sequences and its applications |
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| Authors: | Magda Peligrad Sergey Utev Wei Biao Wu |
| Institution: | Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221-0025 Sergey Utev ; School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, England ; Department of Statistics, The University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637 |
| Abstract: | The paper aims to establish a new sharp Burkholder-type maximal inequality in  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. |
| Keywords: | Martingale maximal inequality Markov chains renewal sequences Bernoulli shifts invariance principle stationary process |
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