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5 matches found
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 times
Nature: Original
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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 906
Keywords: Stopping times, Accessible times, Previsible times
Nature: Original
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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 Potentiel
Keywords: Hunt processes, Previsible times
Nature: Exposition
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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 times
Nature: Original
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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 times
Nature: Original
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