Filtering of derived point processes

Günter Last

Stochastic Processes and their Applications, 1994, vol. 49, issue 2, 297-329

Abstract: We consider two marked point processes [Phi] and [Psi] on the real half-line such that [Psi] is an -predictable thinning and marking of [Phi]. Using the method of the probability of reference we derive linear and non-linear filtering equations for the conditional distribution , where {gt} is a certain -adapted process. In particular, we will apply our results to the filtering of a partially observed semi-Markov process. In that case, the conditional distribution of the last jumptime before t [greater-or-equal, slanted] 0 and the corresponding jumpvalue can be expressed explicitly in terms of a solution of a Markov renewal equation.

Keywords: marked; point; process; derived; point; process; filtering; partially; observed; semi-Markov; process (search for similar items in EconPapers)
Date: 1994
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