This article is cited in 13 papers

Decomposition of optional supermartingales

L. I. Gal'chuk


Abstract: Let $X=(X_t, \mathscr F_t)$ be an optional submartingale of the class $(D)$. It is proved that there exist an optional martingale $m=(m_t, \mathscr F_t)$ and a strongly predictable process $A=(A_t, \mathscr F_t)$ such that the Doob decomposition $X_t=m_t+A_t$ is valid.
Bibliography: 10 titles.

UDC: 519.2

MSC: Primary 60G45; Secondary 60G17, 60G25, 60G40, 60G44

Received: 04.04.1980

 English version: Mathematics of the USSR-Sbornik, 1982, 43:2, 145–158

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