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2014 A note on general sliding window processes
Noga Alon, Ohad Noy Feldheim
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Electron. Commun. Probab. 19: 1-7 (2014). DOI: 10.1214/ECP.v19-3341

Abstract

Let $f:\mathbb{R}^k\to\mathbb{R}$ be a measurable function, and let ${(U_i)}_{i\in\mathbb{N}}$ be a sequence of i.i.d. random variables. Consider the random process $Z_i=f(U_{i},...,U_{i+k-1})$. We show that for all $\ell$, there is a positive probability, uniform in $f$, for $Z_1,...,Z_\ell$ to be monotone. We give upper and lower bounds for this probability, and draw corollaries for $k$-block factor processes with a finite range. The proof is based on an application of combinatorial results from Ramsey theory to the realm of continuous probability.

Citation

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Noga Alon. Ohad Noy Feldheim. "A note on general sliding window processes." Electron. Commun. Probab. 19 1 - 7, 2014. https://doi.org/10.1214/ECP.v19-3341

Information

Accepted: 22 September 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1300.60043
MathSciNet: MR3262072
Digital Object Identifier: 10.1214/ECP.v19-3341

Subjects:
Primary: 60G07
Secondary: 60C05

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