Czechoslovak Mathematical Journal, first online, pp. 1-17


Ergodicity of increments of the Rosenblatt process and some consequences

Petr Čoupek, Pavel Kříž, Bohdan Maslowski

Received May 29, 2023.   Published online March 7, 2024.

Abstract:  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 by additive Rosenblatt noise.
Keywords:  Rosenblatt process; mixing; variation; consistent estimator; random attractor
Classification MSC:  60G22, 37H10

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Affiliations:   Petr Čoupek (corresponding author), Pavel Kříž, Bohdan Maslowski, Charles University, Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics, Sokolovská 49/83, Prague 8 - Karlín, 186 75, Czech Republic, e-mail: coupek@karlin.mff.cuni.cz, kriz@karlin.mff.cuni.cz, maslow@karlin.mff.cuni.cz


 
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