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We prove the local asymptotic mixed normality (LAMN) property for a family ofprobability measures defined by parametrized diffusion processes withnonsynchronous observations. We assume that observation times of processes areindependent of processes and we will study asymptotics when the maximum lengthof observation intervals goes to zero in probability. We also prove that thequasi-maximum likelihood estimator and the Bayes-type estimator proposed inOgihara and Yoshida (Stochastic Process. Appl. 124 (2014) 2954-3008) areasymptotically efficient.

Local asymptotic mixed normality property for nonsynchronously observed diffusion processes