We consider adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones for discretely observed ergodic diffusion processes with observation noise whose variance is constant. The quasi-likelihood functions for the diffusion and drift parameters are introduced and the polynomial-type large deviation inequalities for those quasi-likelihoods are shown to see the asymptotic properties of the adaptive Bayes-type estimators and the convergence of moments for both adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones.

中文翻译：

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遍历扩散加噪声的拟似然分析和贝叶斯型估计量

我们考虑自适应最大似然型估计器和自适应贝叶斯型估计器，用于离散观测的遍历扩散过程，其观测噪声为常数。引入了扩散和漂移参数的拟似然函数，并显示了这些拟似然的多项式型大偏差不等式，以查看自适应贝叶斯型估计量的渐近特性和自适应最大值的矩收敛性 -似然型估计器和自适应贝叶斯型估计器。