SPDEs driven by standard symmetric α-stable cylindrical Lévy processes: Existence, Lyapunov functionals and Itô formula

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

SPDEs driven by standard symmetric α-stable cylindrical Lévy processes: Existence, Lyapunov functionals and Itô formula

Popis výsledku v původním jazyce

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 &amp; ocirc; formula for mild solutions to evolution equations under consideration. The main tools for establishing these results are Yosida approximations and an It &amp; 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.

Název v anglickém jazyce

SPDEs driven by standard symmetric α-stable cylindrical Lévy processes: Existence, Lyapunov functionals and Itô formula

Popis výsledku anglicky

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 &amp; ocirc; formula for mild solutions to evolution equations under consideration. The main tools for establishing these results are Yosida approximations and an It &amp; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Electronic Journal of Probability

ISSN

1083-6489

e-ISSN

1083-6489

Svazek periodika

29

Číslo periodika v rámci svazku

June 2024

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

42

Strana od-do

79

Kód UT WoS článku

001245887900001

EID výsledku v databázi Scopus

2-s2.0-85196715780