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

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.