Filtering of derived point processes
Two marked point processes on the half-line are considered: initial and derived. The derived point process is obtained from the initial one with the help of a thinning and secondary marking procedure. The conditional distribution of the initial (not observable) process till a given time with respect to the derived (observable) process till the same time is investigated. The corresponding filtering equation is derived. In the case of a semi-Markov process as the initial process the corresponding mutual conditional distribution of the last jump-time before a given time and the value just after the jump of the initial process is proved to be a solution of a Markov renewal equation.
scientific article; zbMATH DE number 519772
scientific article