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XVI: 30, 348-354, LNM 920 (1982)
HE, Sheng-Wu; WANG, Jia-Gang
The total continuity of natural filtrations (General theory of processes)
Total continuity of a filtration ${\cal F}$ means that ${\cal F}_T={\cal F}_{T-}$ at every stopping time $T$, not necessarily previsible. It is shown that the filtration of a Lévy process without fixed discontinuities is totally continuous if and only if the jump size is a deterministic function of the jump time. Similarly, the natural filtration of a quasi-left continuous jump process is totally continuous if and only if the size of the $n$-th jump is a deterministic function of the jump times up to the $n$-th. It is shown that under the usual (here called strong'') previsible representation property, quasi-left continuity of the filtration implies total continuity
Keywords: Filtrations, Independent increments, Previsible representation, Total continuity, Lévy processes
Nature: Original
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