Regular Jump Processes and Their Detection and Filtering.
CALIFORNIA UNIV LOS ANGELES SCHOOL OF ENGINEERING AND APPLIED SCIENCE
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A class of regular jump processes RJPs is introduced. A RJP is described in terms of the intensity function of its associated stochastic point process and the state-transition density of its embedded random state sequence. Expressions for the joint occurrence statistics of these processes are derived. Assuming an information stochastic process to causually modulate an observed RJP, the author obtains the joint occurrence statistics of the resulting compound jump processes. The latter is shown to appropriately incorporate the causal MMSE estimates of the conditional intensity and state-transition functions. The results are used to derive a general likelihood-ratio formula for detection, filtering and estimation for RJPs. Author