BILINEAR EQUATIONS IN HILBERT SPACE DRIVEN BY PATHS OF LOW REGULARITY
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10428101" target="_blank" >RIV/00216208:11320/21:10428101 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=GNPXmJDz-S" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=GNPXmJDz-S</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcdsb.2020230" target="_blank" >10.3934/dcdsb.2020230</a>
Alternative languages
Result language
angličtina
Original language name
BILINEAR EQUATIONS IN HILBERT SPACE DRIVEN BY PATHS OF LOW REGULARITY
Original language description
In the article, some bilinear evolution equations in Hilbert space driven by paths of low regularity are considered and solved explicitly. The driving paths are scalar-valued and continuous, and they are assumed to have a finite p-th variation along a sequence of partitions in the sense given by Cont and Perkowski [Trans. Amer. Math. Soc. Ser. B, 6 (2019) 161-186] (p being an even positive integer). Typical functions that satisfy this condition are trajectories of the fractional Brownian motion with Hurst parameter H = 1/p. A strong solution to the bilinear problem is shown to exist if there is a solution to a certain non-autonomous initial value problem. Subsequently, sufficient conditions for the existence of the solution to this initial value problem are given. The abstract results are applied to several stochastic partial differential equations with multiplicative fractional noise, both of the parabolic and hyperbolic type, that are solved explicitly in a pathwise sense.
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete and Continuous Dynamical Systems - Series B
ISSN
1531-3492
e-ISSN
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Volume of the periodical
26
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
34
Pages from-to
121-154
UT code for WoS article
000599420300006
EID of the result in the Scopus database
2-s2.0-85101366931