V: 10, 87-102, LNM 191 (1971)
DELLACHERIE, Claude
Les théorèmes de Mazurkiewicz-Sierpinski et de Lusin (
Descriptive set theory)
Synthetic presentation of (then) little known results on the perfect kernels of closed random sets and uniformization of random sets with countable sections
Comment: See Dellacherie-Meyer,
Probabilités et Potentiel, Chap. XI
Keywords: Analytic sets,
Random sets,
Section theoremsNature: New exposition of known results
Retrieve article from Numdam
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 setNature: Original Retrieve article from Numdam
