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

3

Issued Date

2019-12-01

Resource Type

Article

ISSN

16871847
16871839

DOI

10.1186/s13662-019-2214-1

Other identifier(s)

2-s2.0-85068790131

Rights

Mahidol University

Rights Holder(s)

SCOPUS

Bibliographic Citation

Advances in Difference Equations. Vol.2019, No.1 (2019)

Suggested Citation

P. Vatiwutipong, N. Phewchean Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process. Advances in Difference Equations. Vol.2019, No.1 (2019). doi:10.1186/s13662-019-2214-1 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/51189

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Title

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

Author(s)

P. Vatiwutipong
 N. Phewchean

Other Contributor(s)

South Carolina Commission on Higher Education
 Mahidol University

Abstract

© 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.

Keyword(s)

Mathematics

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URI

https://repository.li.mahidol.ac.th/handle/123456789/51189

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Scopus 2019