Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process

Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process

© 2019, The Author(s). In this paper, we solve the Fokker–Planck equation of the multivariate Ornstein–Uhlenbeck process to obtain its probability density function. This approach allows us to ascertain the distribution without solving it analytically. We find that, at any moment in time, the process...

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Main Authors: P. Vatiwutipong, N. Phewchean
Other Authors: South Carolina Commission on Higher Education
Format: Article
Published: 2020
Subjects:
Mathematics
Online Access:https://repository.li.mahidol.ac.th/handle/123456789/51189
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spelling th-mahidol.511892020-01-27T16:12:05Z Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process P. Vatiwutipong N. Phewchean South Carolina Commission on Higher Education Mahidol University Mathematics © 2019, The Author(s). In this paper, we solve the Fokker–Planck equation of the multivariate Ornstein–Uhlenbeck process to obtain its probability density function. This approach allows us to ascertain the distribution without solving it analytically. We find that, at any moment in time, the process has a multivariate normal distribution. We obtain explicit formulae of mean, covariance, and cross-covariance matrix. Moreover, we obtain its mean-reverting condition and the long-term distribution. 2020-01-27T09:12:05Z 2020-01-27T09:12:05Z 2019-12-01 Article Advances in Difference Equations. Vol.2019, No.1 (2019) 10.1186/s13662-019-2214-1 16871847 16871839 2-s2.0-85068790131 https://repository.li.mahidol.ac.th/handle/123456789/51189 Mahidol University SCOPUS https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85068790131&origin=inward
institution Mahidol University
building Mahidol University Library
continent Asia
country Thailand
Thailand
content_provider Mahidol University Library
collection Mahidol University Institutional Repository
topic Mathematics
spellingShingle Mathematics
P. Vatiwutipong
N. Phewchean
Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process
description © 2019, The Author(s). In this paper, we solve the Fokker–Planck equation of the multivariate Ornstein–Uhlenbeck process to obtain its probability density function. This approach allows us to ascertain the distribution without solving it analytically. We find that, at any moment in time, the process has a multivariate normal distribution. We obtain explicit formulae of mean, covariance, and cross-covariance matrix. Moreover, we obtain its mean-reverting condition and the long-term distribution.
author2 South Carolina Commission on Higher Education
author_facet South Carolina Commission on Higher Education
P. Vatiwutipong
N. Phewchean
format Article
author P. Vatiwutipong
N. Phewchean
author_sort P. Vatiwutipong
title Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process
title_short Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process
title_full Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process
title_fullStr Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process
title_full_unstemmed Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process
title_sort alternative way to derive the distribution of the multivariate ornstein–uhlenbeck process
publishDate 2020
url https://repository.li.mahidol.ac.th/handle/123456789/51189
_version_ 1763488138829758464

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