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Title: Filter Stability in Infinite Dimensional Systems
Authors: Tong, Xin
Advisors: van Handel, Ramon
Contributors: Operations Research and Financial Engineering Department
Keywords: Filter Stability
Fluid models
Infinite Dimensional Systems
Nonlinear filtering
Subjects: Operations research
Issue Date: 2013
Publisher: Princeton, NJ : Princeton University
Abstract: Filtering is a process that sequentially assimilates data from observations and generates a probabilistic description of a hidden underlying process. The goal of this thesis is to study the ergodic behavior of the filtering process in infinite dimensional systems. Such a framework brings recent developments in infinite dimensional systems into the filtering scenario. We approach this goal by introducing an ergodic property named local ergodicity, which generalizes a notion of H. Follmer. This property interacts well with the conditioning structure and hence can be inherited through filtering. We proceed to connect local ergodicity with a topological method developed for infinite dimensional systems named asymptotic coupling. Finally, we show how to apply our framework to fluid models in the forms of stochastic Navier Stokes equations.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Operations Research and Financial Engineering

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