XV: 31, 490-492, LNM 850 (1981)
STRICKER, Christophe
Sur deux questions posées par Schwartz (Stochastic calculus)
Schwartz studied semimartingales in random open sets, and raised two questions: Given a semimartingale $X$ and a random open set $A$, 1) Assume $X$ is increasing in every subinterval of $A$; then is $X$ equal on $A$ to an increasing adapted process on the whole line? 2) Same statement with ``increasing'' replaced by ``continuous''. Schwartz could prove statement 1) assuming $X$ was continuous. It is proved here that 1) is false if $X$ is only cadlag, and that 2) is false in general, though it is true if $A$ is previsible, or only accessible
Keywords: Random sets, Semimartingales in a random open set
Nature: Original
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