Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process
Abstract 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 multiva...
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SpringerOpen
2019-07-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2214-1 |
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doaj-a5172ffdb8574216b6d599390493c3a92020-11-25T02:14:06ZengSpringerOpenAdvances in Difference Equations1687-18472019-07-01201911710.1186/s13662-019-2214-1Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck processP. Vatiwutipong0N. Phewchean1Department of Mathematics, Faculty of Science, Mahidol UniversityDepartment of Mathematics, Faculty of Science, Mahidol UniversityAbstract 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.http://link.springer.com/article/10.1186/s13662-019-2214-1Multivariate Ornstein–Uhlenbeck processMultivariate normal distributionFokker–Planck equationn-dimensional Fourier transform |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
P. Vatiwutipong N. Phewchean |
| spellingShingle |
P. Vatiwutipong N. Phewchean Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process Advances in Difference Equations Multivariate Ornstein–Uhlenbeck process Multivariate normal distribution Fokker–Planck equation n-dimensional Fourier transform |
| author_facet |
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 |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2019-07-01 |
| description |
Abstract 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. |
| topic |
Multivariate Ornstein–Uhlenbeck process Multivariate normal distribution Fokker–Planck equation n-dimensional Fourier transform |
| url |
http://link.springer.com/article/10.1186/s13662-019-2214-1 |
| work_keys_str_mv |
AT pvatiwutipong alternativewaytoderivethedistributionofthemultivariateornsteinuhlenbeckprocess AT nphewchean alternativewaytoderivethedistributionofthemultivariateornsteinuhlenbeckprocess |
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1724902019044474880 |