Open Access
2022 LAMN property for multivariate inhomogeneous diffusions with discrete observations
Ngoc Khue TRAN, Hoang-Long NGO
Author Affiliations +
Electron. J. Statist. 16(2): 4275-4331 (2022). DOI: 10.1214/22-EJS2049


We consider a class of multidimensional inhomogeneous diffusions whose drift coefficient depends on a multidimensional unknown parameter. Under some appropriate assumptions, we prove the local asymptotic mixed normality property for the drift parameter from high-frequency observations when the length of the observation window tends to infinity. To obtain the result, we use the Malliavin calculus techniques and the change of measures. Our approach is applicable for both ergodic and non-ergodic diffusions.


The authors acknowledge support from the Vietnam Institute for Advanced Study in Mathematics (VIASM). H-L. Ngo would like to thank the Hanoi National University of Education for providing a fruitful working environment.


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Ngoc Khue TRAN. Hoang-Long NGO. "LAMN property for multivariate inhomogeneous diffusions with discrete observations." Electron. J. Statist. 16 (2) 4275 - 4331, 2022.


Received: 1 November 2021; Published: 2022
First available in Project Euclid: 17 August 2022

MathSciNet: MR4474575
zbMATH: 07578469
Digital Object Identifier: 10.1214/22-EJS2049

Primary: 60H07 , 60J60
Secondary: 62F12 , 62M05

Keywords: Asymptotic efficiency , local asymptotic mixed normality property , Malliavin calculus , multivariate inhomogeneous diffusion , non-ergodic diffusion

Vol.16 • No. 2 • 2022
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