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.
"LAMN property for multivariate inhomogeneous diffusions with discrete observations." Electron. J. Statist. 16 (2) 4275 - 4331, 2022. https://doi.org/10.1214/22-EJS2049