Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10488202" target="_blank" >RIV/00216208:11320/25:10488202 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=lO-k6UqW9Z" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=lO-k6UqW9Z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.spa.2024.104499" target="_blank" >10.1016/j.spa.2024.104499</a>
Alternative languages
Result language
angličtina
Original language name
Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes
Original language description
In this paper, we study parameter identification for solutions to (possibly non-linear) SDEs driven by additive Rosenblatt process and singularity of the induced laws on the path space. We propose a joint estimator for the drift parameter, diffusion intensity, and Hurst index that can be computed from discrete-time observations with a bounded time horizon and we prove its strong consistency under in-fill asymptotics with a fixed time horizon. As a consequence of this strong consistency, singularity of measures generated by the solutions with different drifts is shown. This results in the invalidity of a Girsanov-type theorem for Rosenblatt processes.
Czech name
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Czech description
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Classification
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
Result continuities
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)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Stochastic Processes and their Applications
ISSN
0304-4149
e-ISSN
1879-209X
Volume of the periodical
179
Issue of the periodical within the volume
January 2025
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
20
Pages from-to
104499
UT code for WoS article
001336114600001
EID of the result in the Scopus database
2-s2.0-85205942165