Pathwise least-squares estimator for linear SPDEs with additive fractional noise
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452091" target="_blank" >RIV/00216208:11320/22:10452091 - isvavai.cz</a>
Alternative codes found
RIV/60461373:22340/22:43924240
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=.ktcy-oym0" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=.ktcy-oym0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1214/22-EJS1990" target="_blank" >10.1214/22-EJS1990</a>
Alternative languages
Result language
angličtina
Original language name
Pathwise least-squares estimator for linear SPDEs with additive fractional noise
Original language description
This paper deals with the drift estimation in linear stochastic evolution equations (with emphasis on linear SPDEs) with additive fractional noise (with Hurst index ranging from 0 to 1) via least-squares procedure. Since the least-squares estimator contains stochastic integrals of divergence type, we address the problem of its pathwise (and robust to observation errors) evaluation by comparison with the pathwise integral of Stratonovich type and using its chain-rule property. The resulting pathwise LSE is then defined implicitly as a solution to a non-linear equation. We study its numerical properties (existence and uniqueness of the solution) as well as statistical properties (strong consistency and the speed of its convergence). The asymptotic properties are obtained assuming fixed time horizon and increasing number of the observed Fourier modes (space asymptotics). We also conjecture the asymptotic normality of the pathwise LSE.
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
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
<a href="/en/project/GA19-07140S" target="_blank" >GA19-07140S: Stochastic Evolution Equations and Space-Time Systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Statistics
ISSN
1935-7524
e-ISSN
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Volume of the periodical
16
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
34
Pages from-to
1561-1594
UT code for WoS article
000825293500028
EID of the result in the Scopus database
2-s2.0-85126761418