CIF:Small: Recursive Estimation of Randomly Modulated Processes

项目摘要：CCF 0916568？CIF：Small：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显示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几个这样的例子。选择一个随机过程来模拟这类现象需要在精确度和复杂性之间进行权衡。该项目研究使用一类称为随机调制过程的通用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，另一个是调制可观测的过程。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一大类随机现象。具体地说，该项目开发了递归估计器，以实时准确地表征互联网流量。估计器的其他重要应用还包括语音处理、核医学、生物学、遗传学和金融。该项目主要研究信号和随机调制过程的参数估计的相互交织的问题。使用度量变换的方法，研究人员正在为这类过程开发递归估计器，并研究求解相关随机微分方程的可行方法。该研究涉及对测量方法的转换与传统的基于似然的方法的深入调查和比较，这些方法总是导致只能离线执行的批处理算法。该项目还涉及随机调制过程的极大似然估计量的渐近性质的推导。递归估计器的实施正在应用于互联网流量跟踪，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.