A martingale approach to modeling, estimation, and detection of jump processes (Ph.D. Thesis abstr.)

Abstract : The study contains a systematic approach to problems of modeling, nonlinear estimation and detection of signals in jump-type observations, namely processes whose paths are discontinuous. It is shown that modern martingale theory provides a powerful tool for attacking these problems in a unified and rigorous manner. A general model for describing signals in jump observations is presented. It is shown that a martingale model includes all the previously proposed ones and also covers the difficult case of past-dependent signals that arises in feedback communication and control problems. (Modified author abstract)