Open Access
Translator Disclaimer
June 2013 Maximum-likelihood estimation for diffusion processes via closed-form density expansions
Chenxu Li
Ann. Statist. 41(3): 1350-1380 (June 2013). DOI: 10.1214/13-AOS1118


This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and accompanied by an algorithm containing only basic and explicit calculations for delivering any arbitrary order of the expansion. The likelihood function is thus approximated explicitly and employed in statistical estimation. The performance of our method is demonstrated by Monte Carlo simulations from implementing several examples, which represent a wide range of commonly used diffusion models. The convergence related to the expansion and the estimation method are theoretically justified using the theory of Watanabe [Ann. Probab. 15 (1987) 1–39] and Yoshida [J. Japan Statist. Soc. 22 (1992) 139–159] on analysis of the generalized random variables under some standard sufficient conditions.


Download Citation

Chenxu Li. "Maximum-likelihood estimation for diffusion processes via closed-form density expansions." Ann. Statist. 41 (3) 1350 - 1380, June 2013.


Published: June 2013
First available in Project Euclid: 4 July 2013

zbMATH: 1273.62196
MathSciNet: MR3113814
Digital Object Identifier: 10.1214/13-AOS1118

Primary: 62F12 , 62M05
Secondary: 60H10 , 60H30 , 60J60

Keywords: asymptotic expansion , diffusion , discrete observation , maximum-likelihood estimation , Transition density

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 3 • June 2013
Back to Top