标题： 在线部分观测扩散过程参数的最大似然估计 显示英文标题

标题： Online Maximum Likelihood Estimation of the Parameters of Partially Observed Diffusion Processes

摘要： 我们重新审视了估计部分观测扩散过程参数的问题，该过程包括一个隐藏状态过程和一个观测过程，具有连续的时间参数。 估计应在在线方式进行，即参数估计应根据观测过滤器递归更新。 我们提供了对不完整数据对数似然函数上的随机梯度上升算法的理论分析。 在关于由状态、滤波器和切滤波器组成的过程的遍历性方面的适当条件下，证明了该算法的收敛性。 此外，我们的参数估计在数值上显示出了改进次优滤波器的潜力，并且即使在系统由于参数冗余而不可识别时也可以应用。 在线参数估计是一个在机器人学、神经科学或金融等领域中普遍存在的具有挑战性的问题，以便为未知或变化的系统设计自适应滤波器和最优控制器。 尽管如此，目前大多数这些算法的收敛性理论分析仍然缺乏。 本文为连续时间中的收敛性理论提供了新的见解。 显示英文摘要

摘要： We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the parameter estimate should be updated recursively based on the observation filtration. We provide a theoretical analysis of the stochastic gradient ascent algorithm on the incomplete-data log-likelihood. The convergence of the algorithm is proved under suitable conditions regarding the ergodicity of the process consisting of state, filter, and tangent filter. Additionally, our parameter estimation is shown numerically to have the potential of improving suboptimal filters, and can be applied even when the system is not identifiable due to parameter redundancies. Online parameter estimation is a challenging problem that is ubiquitous in fields such as robotics, neuroscience, or finance in order to design adaptive filters and optimal controllers for unknown or changing systems. Despite this, theoretical analysis of convergence is currently lacking for most of these algorithms. This article sheds new light on the theory of convergence in continuous time.