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Ergodicity of increments of the Rosenblatt process and some consequences

Petr ČoupekPavel KřížekBohdan Maslowski — 2025

Czechoslovak Mathematical Journal

A new proof of the mixing property of the increments of Rosenblatt processes is given. The proof relies on infinite divisibility of the Rosenblatt law that allows to prove only the pointwise convergence of characteristic functions. Subsequently, the result is used to prove weak consistency of an estimator for the self-similarity parameter of a Rosenblatt process, and to prove the existence of a random attractor for a random dynamical system induced by a stochastic reaction-diffusion equation driven...

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