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

Frank Aurzada; Christian Mönch

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arXiv · 1607.04045

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

Frank Aurzada·Christian Mönch

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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 to compute the persistence exponent for the Rosenblatt process. For general Hermite processes, we derive upper and lower bounds for the persistence probabilites with the conjectured persistence exponent, but with non-matching boundaries.

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BibTeX RIS

Frank Aurzada, Christian Mönch. 2016-07-14. Persistence probabilities and a decorrelation inequality for the Rosenblatt process and Hermite processes. https://arxiv.org/abs/1607.04045

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