CIF:Small: Recursive Estimation of Randomly Modulated Processes

项目摘要：CCF 0916568？CIF：小：随机调制过程的递归估计？在科学和工程中观察到的许多现象都表现出随时间的随机变化。 互联网流量、语音信号和生物信号就是这样的几个例子。 选择一个随机过程来模拟这种现象涉及到准确性与复杂性之间的权衡。本计画研究使用一种称为随机调制过程的多用途随机过程来模拟随机现象的快速计算方法。 随机调制过程由两个更简单的随机过程组成，一个是可观测的，另一个调制可观测的过程。 通过利用随机调制过程的结构特性，研究人员正在设计有效和准确的方法来模拟各种随机现象。具体来说，该项目开发递归估计器，以准确地实时表征互联网流量。 估计器的其他重要应用可以在语音处理、核医学、生物学、遗传学和金融学中找到。该项目侧重于随机调制过程的信号和参数估计的交织问题。 使用变换的措施的方法，调查人员正在开发递归估计等过程，并调查可行的方法来解决相关的随机微分方程。 该研究涉及到深入的调查和比较的措施的方法与传统的基于可能性的方法，总是导致批量算法，只能离线执行的转换。 该项目还涉及随机调制过程的最大似然估计的渐近性质的推导。 递归估计器的实现被应用于互联网流量跟踪，其目的是利用估计器进行网络准入控制和异常检测。

Project Abstract: CCF 0916568?CIF: Small: Recursive Estimation of Randomly Modulated Processes?Many phenomena observed in science and engineering exhibit random variations over time. Internet traffic, speech signals, and biological signals, are a few such examples. Choosing a random process to model such phenomena involves a tradeoff between accuracy versus complexity. This project investigates fast computational methods for modeling random phenomena using a class of versatile random processes called randomly modulated processes. A randomly modulated process consists of two simpler random processes, one which is observable and another which modulates the observable process. By exploiting the structural properties of randomly modulated processes, the investigators are devising efficient and accurate methods to model a wide class of random phenomena. Specifically, the project develops recursive estimators to characterize Internet traffic accurately in real-time. Other important applications of the estimators can be found in speech processing, nuclear medicine, biology, genetics, and finance.The project focuses on the intertwined problems of signal and parameter estimation of randomly modulated processes. Using a transformation of measure approach, the investigators are developing recursive estimators for such processes and investigating feasible approaches for solving the associated stochastic differential equations. The research involves in-depth investigation and comparison of the transformation of measure approach with respect to traditional likelihood-based approaches that lead invariably to batch algorithms that can only be executed offline. The project also involves the derivation of asymptotic properties of maximum likelihood estimators for randomly modulated processes. Implementations of the recursive estimators are being applied to Internet traffic traces, with the objective of leveraging the estimators for network admission control and anomaly detection.