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3 matches found
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 topology
Nature: Original
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VII: 25, 273-283, LNM 321 (1973)
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 816
Keywords: Multiplicative functionals, Multiplicative kernels
Nature: Exposition
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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 functionals
Nature: Original
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