Stochastic integration with respect to fractional processes in Banach spaces

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F22%3A00560670" target="_blank" >RIV/67985556:_____/22:00560670 - isvavai.cz</a>

Alternative codes found

RIV/00216208:11320/22:10444486

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S0022123622000131?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022123622000131?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jfa.2022.109393" target="_blank" >10.1016/j.jfa.2022.109393</a>

Result language

angličtina

Original language name

Stochastic integration with respect to fractional processes in Banach spaces

Original language description

In the article, integration of temporal functions in (possibly non-UMD) Banach spaces with respect to (possibly non-Gaussian) fractional processes from a finite sum of Wiener chaoses is treated. The family of fractional processes that is considered includes, for example, fractional Brownian motions of any Hurst parameter or, more generally, fractionally filtered generalized Hermite processes. The class of Banach spaces that is considered includes a large variety of the most commonly used function spaces such as the Lebesgue spaces, Sobolev spaces, or, more generally, the Besov and Lizorkin-Triebel spaces. In the article, a characterization of the domains of the Wiener integrals on both bounded and unbounded intervals is given for both scalar and cylindrical fractional processes. In general, the integrand takes values in the space of gamma-radonifying operators from a certain homogeneous Sobolev-Slobodeckii space into the considered Banach space. Moreover, an equivalent characterization in terms of a pointwise kernel of the integrand is also given if the considered Banach space is isomorphic with a subspace of a cartesian product of mixed Lebesgue spaces. The results are subsequently applied to stochastic convolution for which both necessary and sufficient conditions for measurability and sufficient conditions for continuity are found. As an application, space-time continuity of the solution to a parabolic equation of order 2m with distributed noise of low time regularity is shown as well as measurability of the solution to the heat equation with Neumann boundary noise of higher regularity.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10103 - Statistics and probability

Project

<a href="/en/project/GA19-07140S" target="_blank" >GA19-07140S: Stochastic Evolution Equations and Space-Time Systems</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2022

Confidentiality

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

Name of the periodical

Journal of Functional Analysis

ISSN

0022-1236

e-ISSN

1096-0783

Volume of the periodical

282

Issue of the periodical within the volume

8

Country of publishing house

US - UNITED STATES

Number of pages

62

Pages from-to

109393

UT code for WoS article

000781239100008

EID of the result in the Scopus database

2-s2.0-85123743515