Contributions to the Theory of Modeling of Stochastic Processes

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This research seeks to develop a theory for recursively updated models for stochastic processes based on covariance data. A general pole-zero structure for the modeling filters is being considered while the order of the filters is permitted to increase with the number of covariance samples. The structure of the filters and the identification schemes to be developed rely on a certain approximate separation principle that applies to the tasks of identifying poles and zeros of a power spectrum. A second issue to be investigated concerns the development of fast algorithms for spectral factorization. Recent advances hold the promise of giving rise to novel and fast spectral factorization algorithms.