Local asymptotic normality for ergodic jump-diffusion processes via transition density approximation

We show local asymptotic normality (LAN) for a statistical model of discretely observed ergodic jump-diffusion processes, where the drift coefficient, diffusion and jump structure are parametrized. Under LAN property, we can discuss efficiency regular estimators, quasi-maximum-likelihood Bayes-type estimators proposed in Shimizu Yoshida (Stat. Inference Stoch. Process. 9 (2006) 227–277) Ogihara 14 (2011) 189–229) shown to be asymptotically efficient this model. Moreover, construct uniformly most powerful tests parameters. Unlike with Aronson-type estimates transition density functions do not hold, which makes it difficult prove LAN. Therefore, instead estimates, employ idea Theorem 1 Jeganathan (Sankhy? Ser. A 44 (1982) 173–212) use L2 regularity condition. that mixed is implied from generated by approximated under suitable conditions. Together approximation means thresholding techniques, property processes proved.