2015/06/24 by Ngoc Khue Tran, Tran, Ngoc Khue
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1506.07270
openalex publication_date 2015/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider an ergodic Ornstein-Uhlenbeck process with jumps\ndriven by a Brownian motion and a compensated Poisson process, whose drift and\ndiffusion coefficients as well as its jump intensity depend on unknown\nparameters. Considering the process discretely observed at high frequency, we\nderive the local asymptotic normality property. To obtain this result,\nMalliavin calculus and Girsanov's theorem are applied to write the\nlog-likelihood ratio in terms of sums of conditional expectations, for which a\ncentral limit theorem for triangular arrays can be applied.\n