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VI: 09, 109-112, LNM 258 (1972)

**SAM LAZARO, José de**; **MEYER, Paul-André**

Un gros processus de Markov. Application à certains flots (Markov processes)

In a vague but useful sense, a ``big'' process over a given process consists of random variables whose values are a part of the path of the original process (the best known example is the excursion process). Here it is shown how the past of a Markov process can be turned into a big (homogeneous) Markov process, and how its semigroup is computed using an idea of Dawson (*Trans. Amer. Math. Soc.*, **131**, 1968)

Comment: For a complete account of Dawson's formula, see Dellacherie-Meyer,*Probabilités et Potentiel,* \no XIV.45

Keywords: Prediction theory, Filtered flows

Nature: Original

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VII: 22, 217-222, LNM 321 (1973)

**MEYER, Paul-André**

Sur les désintégrations régulières de L. Schwartz (General theory of processes)

This paper presents a small part of an important article of L.~Schwartz (*J. Anal. Math.*, **26**, 1973). The main result is an extension of the classical theorem on the existence of regular conditional probability distributions: on a good filtered probability space, the previsible and optional projections of a process can be computed by means of true kernels

Comment: The contents of this paper have been considerably developed by F.~Knight in his theory of prediction. See 1007

Keywords: Previsible projections, Optional projections, Prediction theory

Nature: Exposition, Original additions

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X: 07, 86-103, LNM 511 (1976)

**MEYER, Paul-André**

La théorie de la prédiction de F. Knight (General theory of processes)

This paper is devoted to the work of Knight,*Ann. Prob.* **3**, 1975, the main idea of which is to associate with every reasonable process $(X_t)$ another process, taking values in a space of probability measures, and whose value at time $t$ is a conditional distribution of the future of $X$ after $t$ given its past before $t$. It is shown that the prediction process contains essentially the same information as the original process (which can be recovered from it), and that it is a time-homogeneous Markov process

Comment: The results are related to those of Schwartz (presented in 722), the main difference being that the future is predicted instead of the whole path. Knight has devoted to this subject the*Essays on the Prediction Process,* Hayward Inst. of Math. Stat., 1981, and a book, *Foundations of the Prediction Process,* Oxford Science Publ. 1992

Keywords: Prediction theory

Nature: Exposition, Original additions

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X: 08, 104-117, LNM 511 (1976)

**MEYER, Paul-André**; **YOR, Marc**

Sur la théorie de la prédiction, et le problème de décomposition des tribus ${\cal F}^{\circ}_{t+}$ (General theory of processes)

This paper contains another version of Knight's theory (preceding paper 1007) for cadlag process instead of measurable processes. These results then are applied to the pathology of germ fields: a natural measurability conjecture does not hold, and an example is given of a process $X_t$ such that its natural $\sigma$-field ${\cal F}_{1+}$ is not generated by ${\cal F}_{1}$ and the germ-field at $0$ of the process $(X_{1+s})$

Comment: On the pathology of germ fields, see H. von Weizsäcker,*Ann. Inst. Henri Poincaré,* **19**, 1983

Keywords: Prediction theory, Germ fields

Nature: Original

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XI: 14, 257-297, LNM 581 (1977)

**YOR, Marc**

Sur les théories du filtrage et de la prédiction (General theory of processes, Markov processes)

To be completed

Comment: MR 57, 10801

Keywords: Filtering theory, Prediction theory

Nature: Original

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XII: 27, 398-410, LNM 649 (1978)

**GETOOR, Ronald K.**

Homogeneous potentials (General theory of processes)

This is a development in Knight's prediction theory as described in 1007, 1008. Let $(Z_t^\mu)$ be the prediction process associated with a given measure $\mu$. Then it is shown that a bounded homogeneous right continuous supermartingale (or potential) under $\mu$ remains so under the measures $Z_t^\mu$

Keywords: Prediction theory

Nature: Original

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XV: 22, 307-310, LNM 850 (1981)

**LE JAN, Yves**

Tribus markoviennes et prédiction (Markov processes, General theory of processes)

The problem discussed here is whether a given filtration is generated by a Ray process. The answer is positive under very general conditions. Knight's prediction theory (1007) is used

Keywords: Prediction theory

Nature: Original

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Un gros processus de Markov. Application à certains flots (Markov processes)

In a vague but useful sense, a ``big'' process over a given process consists of random variables whose values are a part of the path of the original process (the best known example is the excursion process). Here it is shown how the past of a Markov process can be turned into a big (homogeneous) Markov process, and how its semigroup is computed using an idea of Dawson (

Comment: For a complete account of Dawson's formula, see Dellacherie-Meyer,

Keywords: Prediction theory, Filtered flows

Nature: Original

Retrieve article from Numdam

VII: 22, 217-222, LNM 321 (1973)

Sur les désintégrations régulières de L. Schwartz (General theory of processes)

This paper presents a small part of an important article of L.~Schwartz (

Comment: The contents of this paper have been considerably developed by F.~Knight in his theory of prediction. See 1007

Keywords: Previsible projections, Optional projections, Prediction theory

Nature: Exposition, Original additions

Retrieve article from Numdam

X: 07, 86-103, LNM 511 (1976)

La théorie de la prédiction de F. Knight (General theory of processes)

This paper is devoted to the work of Knight,

Comment: The results are related to those of Schwartz (presented in 722), the main difference being that the future is predicted instead of the whole path. Knight has devoted to this subject the

Keywords: Prediction theory

Nature: Exposition, Original additions

Retrieve article from Numdam

X: 08, 104-117, LNM 511 (1976)

Sur la théorie de la prédiction, et le problème de décomposition des tribus ${\cal F}^{\circ}_{t+}$ (General theory of processes)

This paper contains another version of Knight's theory (preceding paper 1007) for cadlag process instead of measurable processes. These results then are applied to the pathology of germ fields: a natural measurability conjecture does not hold, and an example is given of a process $X_t$ such that its natural $\sigma$-field ${\cal F}_{1+}$ is not generated by ${\cal F}_{1}$ and the germ-field at $0$ of the process $(X_{1+s})$

Comment: On the pathology of germ fields, see H. von Weizsäcker,

Keywords: Prediction theory, Germ fields

Nature: Original

Retrieve article from Numdam

XI: 14, 257-297, LNM 581 (1977)

Sur les théories du filtrage et de la prédiction (General theory of processes, Markov processes)

To be completed

Comment: MR 57, 10801

Keywords: Filtering theory, Prediction theory

Nature: Original

Retrieve article from Numdam

XII: 27, 398-410, LNM 649 (1978)

Homogeneous potentials (General theory of processes)

This is a development in Knight's prediction theory as described in 1007, 1008. Let $(Z_t^\mu)$ be the prediction process associated with a given measure $\mu$. Then it is shown that a bounded homogeneous right continuous supermartingale (or potential) under $\mu$ remains so under the measures $Z_t^\mu$

Keywords: Prediction theory

Nature: Original

Retrieve article from Numdam

XV: 22, 307-310, LNM 850 (1981)

Tribus markoviennes et prédiction (Markov processes, General theory of processes)

The problem discussed here is whether a given filtration is generated by a Ray process. The answer is positive under very general conditions. Knight's prediction theory (1007) is used

Keywords: Prediction theory

Nature: Original

Retrieve article from Numdam