Integral representation of generalized grey Brownian motion

In this paper, we investigate the representation of a class of non-Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular, the underlying process can be seen...

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Detalles Bibliográficos
Autores principales: Bock, Wolfgang, Desmettre, Sascha, da Silva, José Luís
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Taylor & Francis 2019
Materias:
Articles
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7455069/
https://www.ncbi.nlm.nih.gov/pubmed/32939219
http://dx.doi.org/10.1080/17442508.2019.1641093
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author Bock, Wolfgang
Desmettre, Sascha
da Silva, José Luís
author_facet Bock, Wolfgang
Desmettre, Sascha
da Silva, José Luís
author_sort Bock, Wolfgang
collection PubMed
description In this paper, we investigate the representation of a class of non-Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular, the underlying process can be seen as a non-Gaussian extension of the Ornstein–Uhlenbeck process, hence generalizing the representation results of Muravlev, Russian Math. Surveys 66 (2), 2011 as well as Harms and Stefanovits, Stochastic Process. Appl. 129, 2019 to the non-Gaussian case.
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spelling pubmed-74550692020-09-14 Integral representation of generalized grey Brownian motion Bock, Wolfgang Desmettre, Sascha da Silva, José Luís Stochastics (Abingdon) Articles In this paper, we investigate the representation of a class of non-Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular, the underlying process can be seen as a non-Gaussian extension of the Ornstein–Uhlenbeck process, hence generalizing the representation results of Muravlev, Russian Math. Surveys 66 (2), 2011 as well as Harms and Stefanovits, Stochastic Process. Appl. 129, 2019 to the non-Gaussian case. Taylor & Francis 2019-07-11 /pmc/articles/PMC7455069/ /pubmed/32939219 http://dx.doi.org/10.1080/17442508.2019.1641093 Text en © 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group https://creativecommons.org/licenses/by/4.0/This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Articles
Bock, Wolfgang
Desmettre, Sascha
da Silva, José Luís
Integral representation of generalized grey Brownian motion
title Integral representation of generalized grey Brownian motion
title_full Integral representation of generalized grey Brownian motion
title_fullStr Integral representation of generalized grey Brownian motion
title_full_unstemmed Integral representation of generalized grey Brownian motion
title_short Integral representation of generalized grey Brownian motion
title_sort integral representation of generalized grey brownian motion
topic Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7455069/
https://www.ncbi.nlm.nih.gov/pubmed/32939219
http://dx.doi.org/10.1080/17442508.2019.1641093
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