III: 10, 152-154, LNM 88 (1969)
MEYER, Paul-André
Un résultat élémentaire sur les temps d'arrêt (
General theory of processes)
This useful result asserts that a stopping time is accessible if and only if its graph is contained in a countable union of graphs of previsible stopping times
Comment: Before this was noticed, accessible stopping times were considered important. After this remark, previsible stopping times came to the forefront
Keywords: Stopping times,
Accessible times,
Previsible timesNature: Original
Retrieve article from Numdam
IV: 05, 60-70, LNM 124 (1970)
DELLACHERIE, Claude
Un exemple de la théorie générale des processus (
General theory of processes)
In the case of the smallest filtration for which a given random variable is a stopping time, all the computations of the general theory can be performed explicitly
Comment: This example has become classical. See for example Dellacherie-Meyer,
Probabilités et Potentiel, Chap IV. On the other hand, it can be extended to deal with (unmarked) point processes: see Chou-Meyer
906Keywords: Stopping times,
Accessible times,
Previsible timesNature: Original Retrieve article from Numdam
IX: 34, 530-533, LNM 465 (1975)
MEYER, Paul-André
Sur la démonstration de prévisibilité de Chung et Walsh (
Markov processes)
A new proof of the result that for a Hunt process, the previsible stopping times are exactly those at which the process does not jump was given by Chung-Walsh (
Z. für W-theorie, 29, 1974). Their idea is used here in a modified way, using a formula of Dawson which ``explicitly'' computes conditional expectations and projections. Then it is extended to Ray processes
Comment: The contents of this paper became Chapter XIV
44--47 in Dellacherie-Meyer,
Probabilités et PotentielKeywords: Hunt processes,
Previsible timesNature: Exposition Retrieve article from Numdam
XIV: 34, 316-317, LNM 784 (1980)
ÉMERY, Michel
Une propriété des temps prévisibles (
General theory of processes)
The idea is to prove that the general theory of processes on a random interval $[0,T[$, where $T$ is previsible, is essentially the same as on $[0,\infty[$. To this order, a continuous, strictly increasing adapted process $(A_t)$ is constructed, such that $A_0=0$, $A_T=1$
Keywords: Previsible timesNature: Original Retrieve article from Numdam
XIV: 35, 318-323, LNM 784 (1980)
ÉMERY, Michel
Annonçabilité des temps prévisibles. Deux contre-exemples (
General theory of processes)
It is shown that two standard results on previsible stopping times on a probability space, namely that every previsible time $T$ can be ``foretold'' by a strictly increasing sequence $T_n\uparrow T$, and that the $T_n$ can themselves be taken previsible, become false if exceptional sets of measure zero are not allowed
Keywords: Previsible timesNature: Original Retrieve article from Numdam
