Consistency and asymptotics of a Poisson intensity least-squares estimator for partially observed jump–diffusion processes

A least-squares estimator of the intensity of a Poisson process is studied for a partially observed stochastic system, where the signal evolves as a jump–diffusion process and the observation is a diffusion process. Precisely, we establish the consistency and a central limit theorem of the least-squares estimator when a negative drift coefficient for the jump–diffusion process is considered. We also demonstrate that the variance and the fourth moment of the estimator are bounded but inconsistent when the drift coefficient of the jump diffusion is positive or data is collected within a fixed time horizon.