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from Part IV - Non-Linear Filtering Theory
Published online by Cambridge University Press: 27 May 2021
Here we derive the basic filtering theory for processes with scalar counting-process observations. We discuss optional and predictable projections, introduce the innovation process, and derive the non-linear filtering equations. We also derive the filtering equations for a finite-state Markov chain. We prove a result concerning separation between filtering and detection and we derive the relevant Zakai equation for the unnormalized density.
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