VI: 02, 35-50, LNM 258 (1972)
AZÉMA, Jacques
Une remarque sur les temps de retour. Trois applications (
Markov processes,
General theory of processes)
This paper is the first step in the investigations of Azéma on the ``dual'' form of the general theory of processes (for which see Azéma (
Ann. Sci. ENS, 6, 1973, and
814). Here the $\sigma$-fields of cooptional and coprevisible sets are introduced in a Markovian set-up, and without their definitive names. A section theorem by return times is proved, and applications to the theory of Markov processes are given
Keywords: Homogeneous processes,
Coprevisible processes,
Cooptional processes,
Section theorems,
Projection theorems,
Time reversalNature: Original
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IX: 37, 556-564, LNM 465 (1975)
MEYER, Paul-André
Retour aux retournements (
Markov processes,
General theory of processes)
The first part of the talk is devoted to an important correction to the theorem on p.285 of
814 (Azéma's theory of cooptional and coprevisible sets and its application to Markov processes): the definition of left additive functionals should allow an a.s. explosion at time 0 for initial points belonging to a polar set. The second part belongs to the general theory of processes: if the index set is not the right half-line as usual but the left half-line, the section and projection theorems must be modified in a not quite trivial way
Comment: See Chapter XXVIII of Dellacherie-Maisonneuve-Meyer
Probabilités et potentiel Keywords: Time reversal,
Cooptional processes,
Coprevisible processes,
Homogeneous processesNature: Exposition,
Original additions Retrieve article from Numdam
