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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*TĂ´hoku Math. J.* **28**, 1976

Keywords: Continuous martingales, Krickeberg decomposition

Nature: Original

Retrieve article from Numdam

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

Retrieve article from Numdam

X: 13, 209-215, LNM 511 (1976)

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