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VII: 18, 180-197, LNM 321 (1973)

**MEYER, Paul-André**

Résultats d'Azéma en théorie générale des processus (General theory of processes)

This paper presents several results from a paper of Azéma (*Invent. Math.*, **18**, 1972) which have become (in a slightly extended version) standard tools in the general theory of processes. The problem is that of ``localizing'' a time $L$ which is not a stopping time. With $L$ are associated the supermartingale $c^L_t=P\{L>t|{\cal F}_t\}$ and the previsible increasing processes $p^L$ which generates it (and is the dual previsible projection of the unit mass on the graph of $L$). Then the left support of $dp^L$ is the smallest left-closed previsible set containing the graph of $L$, while the set $\{c^L_-=1\}$ is the greatest previsible set to the left of $L$. Other useful results are the following: given a progressive process $X$, the process $\limsup_{s\rightarrow t} X_s$ is optional, previsible if $s<t$ is added, and a few similar results

Comment: These results have been included (with their optional counterpart, whose interest was discovered later) in Dellacherie-Meyer,*Probabilités et Potentiel*, Vol. E, Chapter XX **12**--17

Keywords: Optimal stopping, Previsible processes

Nature: Exposition

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XII: 33, 457-467, LNM 649 (1978)

**MAINGUENEAU, Marie Anne**

Temps d'arrêt optimaux et théorie générale (General theory of processes)

This is a general discussion of optimal stopping in continuous time. Fairly advanced tools like strong supermartingales, Mertens' decomposition are used

Comment: The subject is taken up in 1332

Keywords: Optimal stopping, Snell's envelope

Nature: Original

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XIII: 32, 378-384, LNM 721 (1979)

**SZPIRGLAS, Jacques**; **MAZZIOTTO, Gérald**

Théorème de séparation dans le problème d'arrêt optimal (General theory of processes)

Let $({\cal G}_t)$ be an enlargement of a filtration $({\cal F}_t)$ with the property that for every $t$, if $X$ is ${\cal G}_t$-measurable, then $E[X\,|\,{\cal F}_t]=E[X\,|\,{\cal F}_\infty]$. Then if $(X_t)$ is a ${\cal F}$-optional process, its Snell envelope is the same in both filtrations. Applications are given to filtering theory

Keywords: Optimal stopping, Snell's envelope, Filtering theory

Nature: Original

Retrieve article from Numdam

Résultats d'Azéma en théorie générale des processus (General theory of processes)

This paper presents several results from a paper of Azéma (

Comment: These results have been included (with their optional counterpart, whose interest was discovered later) in Dellacherie-Meyer,

Keywords: Optimal stopping, Previsible processes

Nature: Exposition

Retrieve article from Numdam

XII: 33, 457-467, LNM 649 (1978)

Temps d'arrêt optimaux et théorie générale (General theory of processes)

This is a general discussion of optimal stopping in continuous time. Fairly advanced tools like strong supermartingales, Mertens' decomposition are used

Comment: The subject is taken up in 1332

Keywords: Optimal stopping, Snell's envelope

Nature: Original

Retrieve article from Numdam

XIII: 32, 378-384, LNM 721 (1979)

Théorème de séparation dans le problème d'arrêt optimal (General theory of processes)

Let $({\cal G}_t)$ be an enlargement of a filtration $({\cal F}_t)$ with the property that for every $t$, if $X$ is ${\cal G}_t$-measurable, then $E[X\,|\,{\cal F}_t]=E[X\,|\,{\cal F}_\infty]$. Then if $(X_t)$ is a ${\cal F}$-optional process, its Snell envelope is the same in both filtrations. Applications are given to filtering theory

Keywords: Optimal stopping, Snell's envelope, Filtering theory

Nature: Original

Retrieve article from Numdam