Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01r781wg09d
 Title: Filter Stability in Infinite Dimensional Systems Authors: Tong, Xin Advisors: van Handel, Ramon Contributors: Operations Research and Financial Engineering Department Keywords: Filter StabilityFluid modelsInfinite Dimensional SystemsNonlinear filtering Subjects: Operations researchMathematics 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. URI: http://arks.princeton.edu/ark:/88435/dsp01r781wg09d 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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