WORKSHOP: Stochastic Filtering and Control

概率论的进步，使新的计算算法成为可能的计算能力的增加，以及统计信号处理、工程和数学金融等重要的现代应用，重新引起了人们对随机滤波和随机控制领域的兴趣。在过去的几年里，他们的理论和实践都取得了重要的进展。在随机滤波中，目标是从部分(可能有噪声的)观测中估计随机过程。应用广泛，例如导弹跟踪和手写识别。在过去的几年里，该领域取得了巨大的进步，主要是因为发现了一套新的强大的算法(序列蒙特卡罗方法或粒子过滤器)。这些新的算法和一个已有40年历史的证明中错误的发现也重新引起了人们对渐近稳定性这个老问题的兴趣，即估计的质量如何依赖于算法的初始化。在随机控制中，目标是最优地控制过程，以便最小化风险函数或等价地最大化效用函数。从结构工程到金融工程，大多数工程领域都会出现这样的问题。然而，最近，随机控制进一步发展的一个巨大推动力是数学金融的新应用的发现，随之而来的是许多新的数学工具的发现，以处理这些新的应用。我们的目标是聚集在这些领域/理论、算法或应用的不同方面以及来自密切相关的随机过滤和随机控制这两个领域的领先研究人员(例如，在部分观察到的过程的控制中)。我们希望，这将使我们更全面地了解已经取得的进展和今后仍面临的挑战。我们认为，不同地区之间存在着相互受精的重大机会。

Advances in probability theory, the increase in computing power that made new computational algorithms possible and important modern applications from statistical signal processing, engineering and mathematical finance have renewed interest in the fields of stochastic filtering and stochastic control. During the last few years, there has been important progress in both their theory and practice. In stochastic filtering, the goal is to estimate a random process from partial (possibly noisy) observations. Applications are widespread, such as missile tracking and handwriting recognition. In the last few years, the field has seen dramatic progress, mainly due to the discovery of a new set of powerful algorithms (sequential Monte Carlo methods or Particle Filters). These new algorithms and the discovery of an error in a forty-year-old proof also renewed interest in the old problem of asymptotic stability, i.e. how the quality of the estimation depends on the initialisation of the algorithm.In stochastic control, the goal is to optimally control a process in order to minimize a risk function or, equivalently, to maximise a utility function. Such problems come up in most fields of engineering, from structural to financial engineering. Recently, however, a huge stimulus to the further development in stochastic control was the discovery of new applications to mathematical finance, which was followed by the discovery of many new mathematical tools created to deal with the new application.We aim to bring together leading researchers working on different aspects of these fields / theory, algorithms or applications / and from both fields of stochastic filtering and stochastic control, which are closely related (for example, in control of partially observed processes). We hope that this will give a fuller picture of the progress that has been made and the challenges that still lie ahead. We believe that there is a significant opportunity for cross-fertilization between the different areas.