On functionals of the Wiener process in a Banach space

On functionals of the Wiener process in a Banach space

In development of stochastic analysis in a Banach space one of the main problem is to establish the existence of the stochastic integral from predictable Banach space valued (operator valued) random process. In the problem of representation of the Wiener functional as a stochastic integral we are fa...

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Main Authors: Badri Mamporia, Omar Purtukhia
Format: Article
Language:English
Published: Elsevier 2018-12-01
Series:Transactions of A. Razmadze Mathematical Institute
Online Access:http://www.sciencedirect.com/science/article/pii/S2346809218301041
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spelling doaj-3145be08ebcb46ada9c1e162dddcf4c02020-11-24T21:07:28ZengElsevierTransactions of A. Razmadze Mathematical Institute2346-80922018-12-011723420428On functionals of the Wiener process in a Banach spaceBadri Mamporia0Omar Purtukhia1Georgian Technical University N. Muskhelishvili Institute of Computational Mathematics, 4 Grigol Peradze st., Tbilisi 0131, Georgia; Corresponding author.Iv. Javakhishvili Tbilisi State University, A.Razmadze Mathematical Institute, Faculty of Exact and Natural Sciences, Department of Mathematics, Tbilisi, GeorgiaIn development of stochastic analysis in a Banach space one of the main problem is to establish the existence of the stochastic integral from predictable Banach space valued (operator valued) random process. In the problem of representation of the Wiener functional as a stochastic integral we are faced with an inverse problem: we have the stochastic integral as a Banach space valued random element and we are looking for a suitable predictable integrand process. There are positive results only for a narrow class of Banach spaces with special geometry (UMD Banach spaces). We consider this problem in a general Banach space for a Gaussian functional. Keywords: Wiener process, Functional of the Wiener process, Ito stochastic integral, Covariance operator in Banach spacehttp://www.sciencedirect.com/science/article/pii/S2346809218301041
collection DOAJ
language English
format Article
sources DOAJ
author Badri Mamporia
Omar Purtukhia
spellingShingle Badri Mamporia
Omar Purtukhia
On functionals of the Wiener process in a Banach space
Transactions of A. Razmadze Mathematical Institute
author_facet Badri Mamporia
Omar Purtukhia
author_sort Badri Mamporia
title On functionals of the Wiener process in a Banach space
title_short On functionals of the Wiener process in a Banach space
title_full On functionals of the Wiener process in a Banach space
title_fullStr On functionals of the Wiener process in a Banach space
title_full_unstemmed On functionals of the Wiener process in a Banach space
title_sort on functionals of the wiener process in a banach space
publisher Elsevier
series Transactions of A. Razmadze Mathematical Institute
issn 2346-8092
publishDate 2018-12-01
description In development of stochastic analysis in a Banach space one of the main problem is to establish the existence of the stochastic integral from predictable Banach space valued (operator valued) random process. In the problem of representation of the Wiener functional as a stochastic integral we are faced with an inverse problem: we have the stochastic integral as a Banach space valued random element and we are looking for a suitable predictable integrand process. There are positive results only for a narrow class of Banach spaces with special geometry (UMD Banach spaces). We consider this problem in a general Banach space for a Gaussian functional. Keywords: Wiener process, Functional of the Wiener process, Ito stochastic integral, Covariance operator in Banach space
url http://www.sciencedirect.com/science/article/pii/S2346809218301041
work_keys_str_mv AT badrimamporia onfunctionalsofthewienerprocessinabanachspace
AT omarpurtukhia onfunctionalsofthewienerprocessinabanachspace
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