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
14Keywords: Time reversal,
Dual semigroupsNature: Exposition
Retrieve article from Numdam
I: 09, 177-189, LNM 39 (1967)
WEIL, Michel
Résolvantes en dualité (
Markov processes,
Potential theory)
Given two sub-Markov resolvents in duality, whose kernels are absolutely continuous with respect to a given measure, it is shown how to choose their densities to get true Green kernels, excessive in one variable and coexcessive in the other one. It is shown also that coexcessive functions are exactly the densities of excessive measures
Comment: These results, now classical, are due to Kunita-T. Watanabe,
Ill. J. Math.,
9, 1965 and
J. Math. Mech.,
15, 1966
Keywords: Green potentials,
Dual semigroupsNature: Exposition Retrieve article from Numdam
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 semigroupsNature: Original Retrieve article from Numdam
III: 09, 144-151, LNM 88 (1969)
MEYER, Paul-André
Un résultat de théorie du potentiel (
Potential theory,
Markov processes)
Under strong duality hypotheses, it is shown that a measure which does not charge polar sets is equivalent to a measure whose Green potential is bounded
Comment: See Meyer,
Processus de Markov, Lecture Notes in M.
26Keywords: Green potentials,
Dual semigroupsNature: Original Retrieve article from Numdam
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 semigroupsNature: Exposition,
Original additions Retrieve article from Numdam
VIII: 19, 329-343, LNM 381 (1974)
SMYTHE, Robert T.
Remarks on the hypotheses of duality (
Markov processes)
To develop the full strength of potential theory, it is helpful to assume that the basic Markov process has a right-continuous, strong Markov dual. The paper investigates what remains if this assumption is not made, i.e., if the process (transient and satisfying the absolute continuity hypothesis (hypothesis (L)) only has a left continuous moderately Markov dual process (Smythe-Walsh ,
Invent. Math.,
19, 1973)
Comment: The independent paper Garsia Alvarez-Meyer
Ann. Prob. 1, 1973, has some results in common with this one
Keywords: Dual semigroupsNature: Original Retrieve article from Numdam
