@article{987764795d52414d8cdb3d123c638bed,
title = "A stochastic fractional Laplace equation driven by colored noise on bounded domain, and its covariance functional",
abstract = "The paper provides conditions for the fractional Laplacian and its spectral representation on stationary Gaussian random fields to be well-defined. In addition, we study existence and uniqueness of the weak solution for a stochastic fractional elliptic equation driven by an additive colored noise over an open bounded set. Both spectral and variational approaches are used to provide a solution. Further, the functional covariance associated with the solution is derived.",
keywords = "colored noise, covariance functional, Fractional Laplacian, generalized random field, spectral representation",
author = "Nicol{\'a}s Pi{\~n}a and Tom{\'a}s Caraballo and Emilio Porcu",
note = "Funding Information: Thanks to IMUS (Instituto de Matem{\'a}ticas Universidad de Sevilla) for partially supported the visit of research assistant, Nicol{\'a}s Pi{\~n}a Le{\'o}n, to the University of Sevilla in 2020. The research of T. Caraballo has been partially supported by Ministerio de Ciencia Innovaci{\'o}n y Universidades (Spain), FEDER (European Community) under grant PGC2018-096540-B-I00, and by FEDER and Junta de Andaluc{\'i}a (Consejer{\'i}a de Econom{\'i}a y Conocimiento) under projects US-1254251 and P18-FR-4509. Agencia de Innovaci{\'o}n y Desarrollo de Andaluc{\'i}a and Spanish Ministry of Science and Innovation Finally, we would like to thank the reviewers for their thoughtful comments and effort toward improving our manuscript. Publisher Copyright: {\textcopyright} 2022 Taylor & Francis Group, LLC.",
year = "2022",
doi = "10.1080/15326349.2022.2045205",
language = "British English",
volume = "38",
pages = "365--389",
journal = "Stochastic Models",
issn = "1532-6349",
publisher = "Taylor and Francis Ltd.",
number = "3",
}