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

Autor:	P. Vatiwutipong, N. Phewchean
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	Multivariate Ornstein–Uhlenbeck process Multivariate normal distribution Fokker–Planck equation n-dimensional Fourier transform Mathematics QA1-939
Zdroj:	Advances in Difference Equations, Vol 2019, Iss 1, Pp 1-7 (2019)
Druh dokumentu:	article
ISSN:	1687-1847
DOI:	10.1186/s13662-019-2214-1
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/a5172ffdb8574216b6d599390493c3a9 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
Nepřihlášeným uživatelům se plný text nezobrazuje	K zobrazení výsledku je třeba se přihlásit.