One-parameter statistical model for linear stochastic differential equation with time delay

Abstract

ABSTRACTAssume that we observe a stochastic process , which satisfies the linear stochastic delay differential equation where a is a finite signed measure on . The local asymptotic properties of the likelihood function are studied. Local asymptotic normality is proved in case of , local asymptotic quadraticity is shown if , and, under some additional conditions, local asymptotic mixed normality or periodic local asymptotic mixed normality is valid if , where is an appropriately defined quantity. As an application, the asymptotic behaviour of the maximum likelihood estimator of based on can be derived as.