Maximal inequality of Stochastic convolution driven by Poisson random measure on Banach spaces

Research output: Working paper

Standard

Maximal inequality of Stochastic convolution driven by Poisson random measure on Banach spaces. / Brzezniak, Zdzislaw; Hausenblas, Erika; Zhu, Jiahui.

2010.

Research output: Working paper

Harvard

Brzezniak, Z, Hausenblas, E & Zhu, J 2010 'Maximal inequality of Stochastic convolution driven by Poisson random measure on Banach spaces'.

APA

Brzezniak, Z., Hausenblas, E., & Zhu, J. (2010). Maximal inequality of Stochastic convolution driven by Poisson random measure on Banach spaces.

Vancouver

Brzezniak Z, Hausenblas E, Zhu J. Maximal inequality of Stochastic convolution driven by Poisson random measure on Banach spaces. 2010 May.

Author

Brzezniak, Zdzislaw ; Hausenblas, Erika ; Zhu, Jiahui. / Maximal inequality of Stochastic convolution driven by Poisson random measure on Banach spaces. 2010.

Bibtex - Download

@techreport{a26cdfc29b73410bb23fc83d851d7fe9,
title = "Maximal inequality of Stochastic convolution driven by Poisson random measure on Banach spaces",
abstract = "Assume that $E$ is an $M$-type $p$ Banach space with $q$-th, $q\geq p$, power of the norm is of $C^2$-class. We consider the stochastic convolution $$u(t)=\int_0^t\int_ZS(t-s)\xi(s,z)\tilde{N}(ds,dz),$$ where $S$ is a $C_0$-semigroup of contractions on $E$ and $\tilde{N}$ is a compensated Poisson random measure. We derive a maximal inequality for a c\`{a}dl\`{a}g modification $\tilde{u}$ of $u$, $$\E\sup_{0\leq s\leq t}|\tilde{u}(s)|_E^{q'}\leq C\ \E\left(\int_0^t\int_Z|\xi(s,z)|_E^{p}N(ds,dz)\right)^{\frac{q'}{p}},$$ for every $00$.",
author = "Zdzislaw Brzezniak and Erika Hausenblas and Jiahui Zhu",
year = "2010",
month = "5",
language = "Undefined/Unknown",
type = "WorkingPaper",

}

RIS (suitable for import to EndNote) - Download

TY - UNPB

T1 - Maximal inequality of Stochastic convolution driven by Poisson random measure on Banach spaces

AU - Brzezniak, Zdzislaw

AU - Hausenblas, Erika

AU - Zhu, Jiahui

PY - 2010/5

Y1 - 2010/5

N2 - Assume that $E$ is an $M$-type $p$ Banach space with $q$-th, $q\geq p$, power of the norm is of $C^2$-class. We consider the stochastic convolution $$u(t)=\int_0^t\int_ZS(t-s)\xi(s,z)\tilde{N}(ds,dz),$$ where $S$ is a $C_0$-semigroup of contractions on $E$ and $\tilde{N}$ is a compensated Poisson random measure. We derive a maximal inequality for a c\`{a}dl\`{a}g modification $\tilde{u}$ of $u$, $$\E\sup_{0\leq s\leq t}|\tilde{u}(s)|_E^{q'}\leq C\ \E\left(\int_0^t\int_Z|\xi(s,z)|_E^{p}N(ds,dz)\right)^{\frac{q'}{p}},$$ for every $00$.

AB - Assume that $E$ is an $M$-type $p$ Banach space with $q$-th, $q\geq p$, power of the norm is of $C^2$-class. We consider the stochastic convolution $$u(t)=\int_0^t\int_ZS(t-s)\xi(s,z)\tilde{N}(ds,dz),$$ where $S$ is a $C_0$-semigroup of contractions on $E$ and $\tilde{N}$ is a compensated Poisson random measure. We derive a maximal inequality for a c\`{a}dl\`{a}g modification $\tilde{u}$ of $u$, $$\E\sup_{0\leq s\leq t}|\tilde{u}(s)|_E^{q'}\leq C\ \E\left(\int_0^t\int_Z|\xi(s,z)|_E^{p}N(ds,dz)\right)^{\frac{q'}{p}},$$ for every $00$.

M3 - Working paper

BT - Maximal inequality of Stochastic convolution driven by Poisson random measure on Banach spaces

ER -