BILINEAR EQUATIONS IN HILBERT SPACE DRIVEN BY PATHS OF LOW REGULARITY

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

BILINEAR EQUATIONS IN HILBERT SPACE DRIVEN BY PATHS OF LOW REGULARITY

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

BILINEAR EQUATIONS IN HILBERT SPACE DRIVEN BY PATHS OF LOW REGULARITY

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA19-07140S" target="_blank" >GA19-07140S: Stochastické evoluční rovnice a časoprostorové systémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Discrete and Continuous Dynamical Systems - Series B

ISSN

1531-3492

e-ISSN

—

Svazek periodika

26

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

34

Strana od-do

121-154

Kód UT WoS článku

000599420300006

EID výsledku v databázi Scopus

2-s2.0-85101366931