A Martingale Approach to Modeling, Estimation and Detection of Jump Processes.
Technical rept. no. 7050-21,
STANFORD UNIV CALIF STANFORD ELECTRONICS LABS
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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
- Statistics and Probability