We consider the problem of tracking an unknown time varying parameter that characterizes the probabilistic evolution of a sequence of independent observations. To this aim, we propose a stochastic gradient descent-based recursive scheme in which the log-likelihood of the observations acts as time varying gain function. We prove convergence in mean-square error in a suitable neighbourhood of the unknown time varying parameter and illustrate the details of our findings in the case where data are generated from distributions belonging to the exponential family.

翻译：我们考虑了追踪一个未知时间差异参数的问题,该参数是独立观测序列概率演进的特点。为此,我们建议采用基于梯度梯度的递归方法,将观测的日志相似性作为时间差异收益函数。我们证明,在未知时间差异参数的合适邻里,正方形误差会趋同,并说明了我们从指数式家庭分布数据中得出的研究结果的细节。</s>