On least-squares estimation for partially observed jump-diffusion processes

We propose a least-squares estimator for the intensity of the Poisson process in 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 and data are streamed online ad infinitum as in a big data scenario. Simulation results are presented to support the theoretical landscape.

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