This article is cited in 6 papers

Short Communications

Persistence probabilities and a decorrelation inequality for the Rosenblatt process and Hermite processes

F. Aurzada, C. Mönch

Technische Universität Darmstadt, FB Mathematik, Schlossgartenstr., 7, 64289 Darmstadt, Germany

Abstract: We study persistence probabilities of Hermite processes. As a tool, we derive a general decorrelation inequality for the Rosenblatt process, which is reminiscent of Slepian's lemma for Gaussian processes or the FKG inequality and which may be of independent interest. This allows us to compute the persistence exponent for the Rosenblatt process. For general Hermite processes, we derive upper and lower bounds for the persistence probabilities with the conjectured persistence exponent, but with nonmatching boundaries.

Keywords: long-range dependence, persistence, random walk, Hermite process, Rosenblatt process, correlation inequality, first passage times.

Received: 02.02.2017
Revised: 20.01.2018
Accepted: 06.03.2018

Language: English

DOI: 10.4213/tvp5137

 English version: Theory of Probability and its Applications, 2019, 63:4, 664–670

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