VI: 22, 233-242, LNM 258 (1972)
WALSH, John B.
The perfection of multiplicative functionals (
Markov processes)
In the definition of multiplicative functionals the problem arose from the beginning whether the exceptional null set in the relation $M_{s+t}=M_s\,M_t\circ\theta_s$ was allowed to depend on $s$ or not---in the latter case the functional is said to be perfect. C.~Doléans showed by a detailed analysis (see
203) that every functional has a perfect modification, see also Dellacherie
304. Here a perfect version is constructed directly as $\lim_{s\rightarrow 0} M_{t-s}\circ\theta_s$, the limit being taken in the essential topology of the line, which ignores sets of zero Lebesgue measure
Keywords: Multiplicative functionals,
Perfection,
Essential topologyNature: Original
Retrieve article from Numdam
VII: 25, 273-283, LNM 321 (1973)
PINSKY, Mark A.
Fonctionnelles multiplicatives opératrices (
Markov processes)
This paper presents results due to the author (
Advances in Probability, 3, 1973). The essential idea is to consider multiplicative functionals of a Markov process taking values in the algebra of bounded operators of a Banach space $L$. Such a functional defines a semi-group acting on bounded $L$-valued functions. This semi-group determines the functional. The structure of functionals is investigated in the case of a finite Markov chain. The case where $L$ is finite dimensional and the Markov process is Browian motion is investigated too. Asymptotic results near $0$ are described
Comment: This paper explores the same idea as Jacod (
Mém. Soc. Math. France, 35, 1973), though in a very different way. See
816Keywords: Multiplicative functionals,
Multiplicative kernelsNature: Exposition Retrieve article from Numdam
VIII: 01, 1-10, LNM 381 (1974)
AZÉMA, Jacques;
MEYER, Paul-André
Une nouvelle représentation du type de Skorohod (
Markov processes)
A Skorohod imbedding theorem for general Markov processes is proved, in which the stopping time is a randomized ``left'' terminal time. A uniqueness result is proved
Comment: The result is deduced from a representation of measures by left additive functionals, due to Azéma (
Invent. Math. 18, 1973 and this volume,
814). A general survey on the Skorohod embedding problem is Ob\lój,
Probab. Surv. 1, 2004
Keywords: Skorohod imbedding,
Multiplicative functionalsNature: Original Retrieve article from Numdam
