A note on space time Holder regularity of mild solutions to stochastic Cauchy problems in L-p-spaces

Título traducido de la contribución: Una nota sobre la regularidad del sostenedor del espacio-tiempo de las soluciones suaves a los problemas estocásticos Cauchy en los espacios Lp

Resultado de la investigación: Contribución a RevistaArtículo

1 Cita (Scopus)

Resumen

Este trabajo revisa la regularidad de Hölder de las soluciones suaves de los problemas del Cauchy estocástico parabólico en los espacios de Lebesgue Lp(O), con p≥ y O⊂Rd como un dominio delimitado. Encontramos condiciones sobre p,β y γ bajo las cuales la solución suave tiene casi seguramente trayectorias en Cβ([0,T];Cγ(O)). Estas condiciones no dependen del espacio Cameron-Martin Hilbert asociado al ruido cilíndrico de accionamiento. La herramienta principal de este estudio es un resultado de regularidad para las convoluciones estocásticas en espacios Banach tipo M 2 por Brzeźniak (Stochastics Stochastics Rep.61 (1997) 245-295).
Idioma originalEnglish (US)
Páginas (desde-hasta)767-777
Número de páginas10
PublicaciónBrazilian Journal of Probability and Statistics
Volumen29
N.º4
DOI
EstadoPublished - abr 2014

Citar esto

@article{e9ad4161a6124364aae68a51b8570b96,
title = "A note on space time Holder regularity of mild solutions to stochastic Cauchy problems in L-p-spaces",
abstract = "This paper revisits the H{\"o}lder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces Lp(O), with p≥2 and O⊂Rd a a bounded domain. We find conditions on p,β and γ under which the mild solution has almost surely trajectories in Cβ([0,T];Cγ(O)). These conditions do not depend on the Cameron–Martin Hilbert space associated with the driving cylindrical noise. The main tool of this study is a regularity result for stochastic convolutions in M-type 2 Banach spaces by Brzeźniak (Stochastics Stochastics Rep.61 (1997) 245–295).",
author = "Rafael Serrano",
year = "2014",
month = "4",
doi = "10.1214/14-BJPS245",
language = "English (US)",
volume = "29",
pages = "767--777",
journal = "Brazilian Journal of Probability and Statistics",
issn = "0103-0752",
publisher = "Associacao Brasileira de Estatistica",
number = "4",

}

A note on space time Holder regularity of mild solutions to stochastic Cauchy problems in L-p-spaces. / Serrano, Rafael.

En: Brazilian Journal of Probability and Statistics, Vol. 29, N.º 4, 04.2014, p. 767-777.

Resultado de la investigación: Contribución a RevistaArtículo

TY - JOUR

T1 - A note on space time Holder regularity of mild solutions to stochastic Cauchy problems in L-p-spaces

AU - Serrano, Rafael

PY - 2014/4

Y1 - 2014/4

N2 - This paper revisits the Hölder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces Lp(O), with p≥2 and O⊂Rd a a bounded domain. We find conditions on p,β and γ under which the mild solution has almost surely trajectories in Cβ([0,T];Cγ(O)). These conditions do not depend on the Cameron–Martin Hilbert space associated with the driving cylindrical noise. The main tool of this study is a regularity result for stochastic convolutions in M-type 2 Banach spaces by Brzeźniak (Stochastics Stochastics Rep.61 (1997) 245–295).

AB - This paper revisits the Hölder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces Lp(O), with p≥2 and O⊂Rd a a bounded domain. We find conditions on p,β and γ under which the mild solution has almost surely trajectories in Cβ([0,T];Cγ(O)). These conditions do not depend on the Cameron–Martin Hilbert space associated with the driving cylindrical noise. The main tool of this study is a regularity result for stochastic convolutions in M-type 2 Banach spaces by Brzeźniak (Stochastics Stochastics Rep.61 (1997) 245–295).

U2 - 10.1214/14-BJPS245

DO - 10.1214/14-BJPS245

M3 - Article

VL - 29

SP - 767

EP - 777

JO - Brazilian Journal of Probability and Statistics

JF - Brazilian Journal of Probability and Statistics

SN - 0103-0752

IS - 4

ER -