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 functionalsNature: Exposition,
Original additions
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