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 decompositionNature: Original
Retrieve article from Numdam
