Ergodicity of increments of the Rosenblatt process and some consequences

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10488204" target="_blank" >RIV/00216208:11320/25:10488204 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=FI20VPoW9-" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=FI20VPoW9-</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/CMJ.2024.0252-23" target="_blank" >10.21136/CMJ.2024.0252-23</a>

Result language
angličtina
Original language name
Ergodicity of increments of the Rosenblatt process and some consequences
Original language description
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.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability

Project
<a href="/en/project/GA22-12790S" target="_blank" >GA22-12790S: Stochastic systems in infinite dimensions</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)