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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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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

Retrieve article from Numdam

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

Keywords: Continuous martingales, Krickeberg decomposition

Nature: Original

Retrieve article from Numdam

XIII: 27, 307-312, LNM 721 (1979)

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

Keywords: Weighted norm inequalities, Burkholder inequalities

Nature: Original

Retrieve article from Numdam