Ergodicity of increments of the Rosenblatt process and some consequences

Petr Čoupek; Pavel Křížek; Bohdan Maslowski

Czechoslovak Mathematical Journal (2025)

  • Issue: 1, page 327-343
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Čoupek, Petr, Křížek, Pavel, and Maslowski, Bohdan. "Ergodicity of increments of the Rosenblatt process and some consequences." Czechoslovak Mathematical Journal (2025): 327-343. <http://eudml.org/doc/299927>.

@article{Čoupek2025,
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.},
author = {Čoupek, Petr, Křížek, Pavel, Maslowski, Bohdan},
journal = {Czechoslovak Mathematical Journal},
keywords = {Rosenblatt process; mixing; variation; consistent estimator; random attractor},
language = {eng},
number = {1},
pages = {327-343},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Ergodicity of increments of the Rosenblatt process and some consequences},
url = {http://eudml.org/doc/299927},
year = {2025},
}

TY - JOUR
AU - Čoupek, Petr
AU - Křížek, Pavel
AU - Maslowski, Bohdan
TI - Ergodicity of increments of the Rosenblatt process and some consequences
JO - Czechoslovak Mathematical Journal
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 327
EP - 343
AB - 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.
LA - eng
KW - Rosenblatt process; mixing; variation; consistent estimator; random attractor
UR - http://eudml.org/doc/299927
ER -

References

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