VI: 07, 101-104, LNM 258 (1972)
KAZAMAKI, Norihiko
Krickeberg's decomposition for local martingales (Martingale theory)
It is shown that a local martingale bounded in $L^1$ is a difference of two (minimal) positive local martingales
Keywords: Local martingales, Krickeberg decomposition
Nature: Original
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X: 13, 209-215, LNM 511 (1976)
SEKIGUCHI, Takesi
On the Krickeberg decomposition of continuous martingales (Martingale theory)
The problem investigated is whether the two positive martingales occurring in the Krickeberg decomposition of a $L^1$-bounded continuous martingale of a filtration $({\cal F}_t)$ are themselves continuous. It is shown that the answer is yes only under very stringent conditions: there exists a sub-filtration $({\cal G}_t)$ such that 1) all ${\cal G}$-martingales are continuous 2) the continuous ${\cal F}$-martingales are exactly the ${\cal G}$-martingales
Comment: For related work of the author see Tôhoku Math. J. 28, 1976
Keywords: Continuous martingales, Krickeberg decomposition
Nature: Original
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