In this paper, we consider a general partially observed diffusion model with periodic coefficients and with non-degenerate diffusion component. The coefficients of such a model depend on an unknown (static and deterministic) parameter which needs to be estimated based on the observed component of the diffusion process. We show that, under a minimal assumption of identifiability, and given enough regularity of the diffusion coefficients, a maximum likelihood estimator of the unknown parameter converges to the true parameter value as the sample size grows to infinity.

翻译：本文研究一类具有周期系数且扩散项非退化的广义部分观测扩散模型。该模型的系数依赖于一个未知（静态且确定性）参数，需要根据扩散过程的观测分量进行估计。我们证明，在可辨识性的最小假设下，并给定扩散系数足够的正则性，当样本量趋于无穷时，未知参数的最大似然估计量收敛于真实参数值。