Ergodicity and parameter estimates for infinite-dimensional fractional Ornstein-Uhlenbeck process
Result description
In this paper we prove the existence of the strictly stationary solution for stochastic evolution equation driven by fractional Brownian motion which solution is an infinite-dimensional fractional Ornstein-Uhlenbeck process. We prove the ergodic theoremsfor a strictly stationary solution as well as for an arbitrary solution. Based on ergodicity, we present several results in parameter estimates in infinite dimensional equations.
Keywords
stochastic partial differential equationsfractional Brownian motionfractional Ornstein-Uhlenbeck processstrictly stationary solutionergodicityparameter estimates
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/67985840:_____/08:00319526
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Ergodicity and parameter estimates for infinite-dimensional fractional Ornstein-Uhlenbeck process
Original language description
In this paper we prove the existence of the strictly stationary solution for stochastic evolution equation driven by fractional Brownian motion which solution is an infinite-dimensional fractional Ornstein-Uhlenbeck process. We prove the ergodic theoremsfor a strictly stationary solution as well as for an arbitrary solution. Based on ergodicity, we present several results in parameter estimates in infinite dimensional equations.
Czech name
Ergodicity and parameter estimates for infinite-dimensional fractional Ornstein-Uhlenbeck process
Czech description
Dokážeme existenci a ergodicitu striktně stacionárního řešení pro lineární stochastické evoluční rovnice řízené cylindrickým frakcionálním Brownovým pohybem. Studujeme také ergodické chování nestacionárního nekonečně dimenzionálního frakcionálního Ornstein-Uhlenbeckova procesu. Na základě těchto výsledků ukážeme silnou konzistenci vhodně definované rodiny odhadu parametrů. Obecné výsledky pak aplikujeme na lineární parabolické a hyperbolické rovnice perturbované frakcionálním šumem.
Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2008
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applied Mathematics and Optimization
ISSN
0095-4616
e-ISSN
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Volume of the periodical
57
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
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UT code for WoS article
000256083900006
EID of the result in the Scopus database
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Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2008