SPDEs driven by standard symmetric α-stable cylindrical Lévy processes: Existence, Lyapunov functionals and Itô formula
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10491191" target="_blank" >RIV/00216208:11320/24:10491191 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=72x.mfrzWB" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=72x.mfrzWB</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1214/24-EJP1136" target="_blank" >10.1214/24-EJP1136</a>
Alternative languages
Result language
angličtina
Original language name
SPDEs driven by standard symmetric α-stable cylindrical Lévy processes: Existence, Lyapunov functionals and Itô formula
Original language description
We investigate several aspects of solutions to stochastic evolution equations in Hilbert spaces driven by a standard symmetric alpha -stable cylindrical noise. Similarly to cylindrical Brownian motion or Gaussian white noise, standard symmetric alpha -stable noise exists only in a generalised sense in Hilbert spaces. The main results of this work are the existence of a mild solution, long-term regularity of the solutions via Lyapunov functional approach, and an It & ocirc; formula for mild solutions to evolution equations under consideration. The main tools for establishing these results are Yosida approximations and an It & ocirc; formula for Hilbert space -valued semi -martingales where the martingale part is represented as an integral driven by cylindrical alpha -stable noise. While these tools are standard in stochastic analysis, due to the cylindrical nature of our noise, their application requires completely novel arguments and techniques.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
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 Probability
ISSN
1083-6489
e-ISSN
1083-6489
Volume of the periodical
29
Issue of the periodical within the volume
June 2024
Country of publishing house
US - UNITED STATES
Number of pages
42
Pages from-to
79
UT code for WoS article
001245887900001
EID of the result in the Scopus database
2-s2.0-85196715780