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2 matches found
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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XIII: 27, 307-312, LNM 721 (1979)
IZUMISAWA, Masataka; SEKIGUCHI, Takesi
Weighted norm inequalities for martingales (Martingale theory)
See the review of 1326. The topic is the same, though the proof is different
Comment: See the paper by Kazamaki-Izumisawa in Tôhoku Math. J. 29, 1977. For a modern reference see also Kazamaki, Continuous Exponential Martingales and $\,BMO$, LNM. 1579, 1994
Keywords: Weighted norm inequalities, Burkholder inequalities
Nature: Original
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