STOCHASTIC POROUS MEDIA EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10190421" target="_blank" >RIV/00216208:11320/13:10190421 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1142/S021949371350010X" target="_blank" >http://dx.doi.org/10.1142/S021949371350010X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S021949371350010X" target="_blank" >10.1142/S021949371350010X</a>

Jazyk výsledku

angličtina

Název v původním jazyce

STOCHASTIC POROUS MEDIA EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION

Popis výsledku v původním jazyce

The present work deals with stochastic porous media equation with multiplicative noise, driven by fractional Brownian motion B-(H) with Hurst index H > 1/2. The stochastic integral with integrator B-(H) is defined pathwise following the theory developedby Zahle [24], based on the so-called fractional derivatives. It is shown that there is a one-to-one correspondence between solutions to the stochastic equation and solutions to its deterministic counterpart. By means of this correspondence and exploiting properties of the deterministic porous media equation, the existence, uniqueness, regularity and long-time properties of the solution is established. We also prove that the solution forms a random dynamical system in an appropriate function space.

Název v anglickém jazyce

STOCHASTIC POROUS MEDIA EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION

Popis výsledku anglicky

The present work deals with stochastic porous media equation with multiplicative noise, driven by fractional Brownian motion B-(H) with Hurst index H > 1/2. The stochastic integral with integrator B-(H) is defined pathwise following the theory developedby Zahle [24], based on the so-called fractional derivatives. It is shown that there is a one-to-one correspondence between solutions to the stochastic equation and solutions to its deterministic counterpart. By means of this correspondence and exploiting properties of the deterministic porous media equation, the existence, uniqueness, regularity and long-time properties of the solution is established. We also prove that the solution forms a random dynamical system in an appropriate function space.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP201%2F10%2F0752" target="_blank" >GAP201/10/0752: Stochastické časoprostorové systémy</a><br>

Návaznosti

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

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

Stochastics and Dynamics

ISSN

0219-4937

e-ISSN

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Svazek periodika

13

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

33

Strana od-do

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Kód UT WoS článku

000325407900007

EID výsledku v databázi Scopus

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