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8 matches found
I: 08, 166-176, LNM 39 (1967)
WEIL, Michel
Retournement du temps dans les processus markoviens (Markov processes)
This talk presents the now classical results of Nagasawa (Nagoya Math. J., 24, 1964) extending to continuous time the results proved by Hunt in discrete time on time reversal of a Markov process at an L-time'' or return time
Comment: See also 202. These results have been essentially the best ones until they were extended to Kuznetsov measures, see Dellacherie-Meyer, Probabilités et Potentiel, chapter XIX 14
Keywords: Time reversal, Dual semigroups
Nature: Exposition
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II: 02, 22-33, LNM 51 (1968)
CARTIER, Pierre; MEYER, Paul-André; WEIL, Michel
Le retournement du temps~: compléments à l'exposé de M.~Weil (Markov processes)
In 108, M.~Weil had presented the work of Nagasawa on the time reversal of a Markov process at a L-time'' or return time. Here the results are improved on three points: a Markovian filtration is given for the reversed process; an analytic condition on the semigroup is lifted; finally, the behaviour of the coexcessive functions on the sample functions of the original process is investigated
Comment: The results of this paper have become part of the standard theory of time reversal. See 312 for a correction
Keywords: Time reversal, Dual semigroups
Nature: Original
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III: 12, 160-162, LNM 88 (1969)
MEYER, Paul-André
Rectification à des exposés antérieurs (Markov processes, Martingale theory)
Corrections are given to the talk 202 by Cartier, Meyer and Weil and to the talk 106 by Meyer
Comment: This note introduces Walsh's fork'', the well-known strong Markov process whose dual is not strong Markov
Keywords: Time reversal, Stochastic integrals
Nature: Correction
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V: 22, 213-236, LNM 191 (1971)
MEYER, Paul-André
Le retournement du temps, d'après Chung et Walsh (Markov processes)
The paper of Chung and Walsh (Acta Math., 134, 1970) proved that any right continuous strong Markov process had a reversed left continuous moderate Markov process at any $L$-time, with a suitably constructed dual semigroup. Appendix 1 gives a useful characterization of càdlàg processes using stopping times (connected with amarts). Appendix 2 proves (following Mokobodzki) that any excessive function strongly dominated by a potential of function is such a potential
Comment: The theorem of Chung-Walsh remains the deepest on time reversal (to be supplemented by the consideration of Kuznetsov's measures)
Keywords: Time reversal, Dual semigroups
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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 reversal
Nature: Original
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VIII: 14, 262-288, LNM 381 (1974)
MEYER, Paul-André
Les travaux d'Azéma sur le retournement du temps (General theory of processes, Markov processes)
This paper is an exposition of a paper by Azéma (Ann. Sci. ENS, 6, 1973) in which the theory dual'' to the general theory of processes was developed. It is shown first how the general theory itself can be developed from a family of killing operators, and then how the dual theory follows from a family of shift operators $\theta_t$. A transience hypothesis involving the existence of many return times'' permits the construction of a theory completely similar to the usual one. Then some of Azéma's applications to the theory of Markov processes are given, particularly the representation of a measure not charging $\mu$-polar sets as expectation under the initial measure $\mu$ of a left additive functional
Comment: This paper follows (with considerable progress) the line of 602. The names given by Azéma to right and left additive functionals are exchanged. Another difference with Azéma's original paper is the fact that the lifetime $\zeta$ does not appear. All these results have been included in Dellacherie-Maisonneuve-Meyer, Probabilités et Potentiel, Chapter XVIII, 1992
Keywords: Time reversal, Shift operators, Killing operators, Cooptional processes, Coprevisible processes, Additive functionals, Left additive functionals
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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 processes
A simple example is given of a continuous semimartingale (a Brownian motion which stops at time $1$ and starts moving again at time $T>1$, $T$ encoding all the information up to time $1$) whose reversed process is not a semimartingale