Summary
Real valued càdlàg processes are viewed in the manner described in [2], as random elements of D(R) which is endowed with the J 1 topology. We consider a sequence of point processes (N n, \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathfrak{F}}\) n* , ℱ, P) n≧1 with their minimal filtrations, together with their compensators A n, \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathfrak{F}}\) n* , ℱ, P) n≧1. Under slightly stronger assumptions than N n⇒N and A n⇒A, we show that A has the same distribution in D(R) as the compensator of N for the filtration generated by N and A.
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Schiopu-Kratina, I. Weak convergence of processes in D(R) and compensation of point processes. Probab. Th. Rel. Fields 72, 99–109 (1986). https://doi.org/10.1007/BF00343898
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DOI: https://doi.org/10.1007/BF00343898
Keywords
- Filtration
- Stochastic Process
- Probability Theory
- Statistical Theory
- Point Process