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V: 29, 290-310, LNM 191 (1971)

**WALSH, John B.**

Some topologies connected with Lebesgue measure (Markov processes, General theory of processes, Potential theory)

It is a recurrent theme in the theory of stochastic processes that time sets of measure $0$ should be ignored. Thus topologies on the line which ignore sets of measure $0$ are useful. The main topic here is the so-called*essential topology,* used in the paper of Chung and Walsh 522 in the same volume

Comment: See Doob*Bull. Amer. Math. Soc.*, **72**, 1966. An important application in given by Walsh 623 in the next volume. See the paper 1025 of Benveniste. For the use of a different topology see Ito *J. Math. Soc. Japan,* **20**, 1968

Keywords: Essential topology

Nature: Original

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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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VI: 23, 243-252, LNM 258 (1972)

**MEYER, Paul-André**

Quelques autres applications de la méthode de Walsh (``La perfection en probabilités'') (Markov processes)

This is but an exercise on using the method of the preceding paper 622 to reduce the exceptional sets in other situations: additive functionals, cooptional times and processes, etc

Comment: A correction to this paper is mentioned on the errata list of vol. VII

Keywords: Additive functionals, Return times, Essential topology

Nature: Original

Retrieve article from Numdam

Some topologies connected with Lebesgue measure (Markov processes, General theory of processes, Potential theory)

It is a recurrent theme in the theory of stochastic processes that time sets of measure $0$ should be ignored. Thus topologies on the line which ignore sets of measure $0$ are useful. The main topic here is the so-called

Comment: See Doob

Keywords: Essential topology

Nature: Original

Retrieve article from Numdam

VI: 22, 233-242, LNM 258 (1972)

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

Retrieve article from Numdam

VI: 23, 243-252, LNM 258 (1972)

Quelques autres applications de la méthode de Walsh (``La perfection en probabilités'') (Markov processes)

This is but an exercise on using the method of the preceding paper 622 to reduce the exceptional sets in other situations: additive functionals, cooptional times and processes, etc

Comment: A correction to this paper is mentioned on the errata list of vol. VII

Keywords: Additive functionals, Return times, Essential topology

Nature: Original

Retrieve article from Numdam