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V: 17, 177-190, LNM 191 (1971)

**MEYER, Paul-André**

Processus de Poisson ponctuels d'après K. Ito (Markov processes, Point processes)

Presents (a preliminary form of) the celebrated paper of Ito (*Proc. Sixth Berkeley Symposium,* **3**, 1972) on excursion theory, with an extension (the use of possibly unbounded entrance laws instead of initial measures) which has become part of the now classical theory

Comment: A slip in the definition of Poisson point processes is corrected in vol. VI p.253. The material has appeared repeatedly in book form

Keywords: Poisson point processes, Excursions, Local times

Nature: Exposition, Original additions

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X: 01, 1-18, LNM 511 (1976)

**BRÉMAUD, Pierre**

La méthode des semi-martingales en filtrage quand l'observation est un processus ponctuel marqué (Martingale theory, Point processes)

This paper discusses martingale methods (as developed by Jacod,*Z. für W-theorie,* **31,** 1975) in the filtering theory of point processes

Comment: The author has greatly developed this topic in his book*Poisson Processes and Queues,* Springer 1981

Keywords: Point processes, Previsible representation, Filtering theory

Nature: Original

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XV: 23, 311-319, LNM 850 (1981)

**ALDOUS, David J.**; **BARLOW, Martin T.**

On countable dense random sets (General theory of processes, Point processes)

This paper is devoted to random sets $B$ which are countable, optional (i.e., can be represented as the union of countably many graphs of stopping times $T_n$) and dense. The main result is that whenever the increasing processes $I_{t\ge T_n}$ have absolutely continuous compensators (in which case the same property holds for any stopping time $T$ whose graph is contained in $B$), then the random set $B$ can be represented as the union of all the points of countably many independent standard Poisson processes (intuitively, a Poisson measure whose rate is $+\infty$ times Lebesgue measure). This may require, however, an innocuous enlargement of filtration. Another characterization of such random sets is roughly that they do not intersect previsible sets of zero Lebesgue measure. Note also an interesting example of a set optional w.r.t. two filtrations, but not w.r.t. their intersection

Keywords: Poisson point processes

Nature: Original

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XX: 02, 28-29, LNM 1204 (1986)

**FAGNOLA, Franco**; **LETTA, Giorgio**

Sur la représentation intégrale des martingales du processus de Poisson (Stochastic calculus, Point processes)

Dellacherie gave in 805 a proof by stochastic calculus of the previsible representation property for the Wiener and Poisson processes. A gap in this proof is filled in 928 for Brownian motion and here for Poisson processes

Keywords: Stochastic integrals, Previsible representation, Poisson processes

Nature: Correction

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XLIII: 14, 341-349, LNM 2006 (2011)

**BOULEAU, Nicolas**

The Lent Particle Method for Marked Point Processes (General theory of processes, Point processes)

Nature: Original

Processus de Poisson ponctuels d'après K. Ito (Markov processes, Point processes)

Presents (a preliminary form of) the celebrated paper of Ito (

Comment: A slip in the definition of Poisson point processes is corrected in vol. VI p.253. The material has appeared repeatedly in book form

Keywords: Poisson point processes, Excursions, Local times

Nature: Exposition, Original additions

Retrieve article from Numdam

X: 01, 1-18, LNM 511 (1976)

La méthode des semi-martingales en filtrage quand l'observation est un processus ponctuel marqué (Martingale theory, Point processes)

This paper discusses martingale methods (as developed by Jacod,

Comment: The author has greatly developed this topic in his book

Keywords: Point processes, Previsible representation, Filtering theory

Nature: Original

Retrieve article from Numdam

XV: 23, 311-319, LNM 850 (1981)

On countable dense random sets (General theory of processes, Point processes)

This paper is devoted to random sets $B$ which are countable, optional (i.e., can be represented as the union of countably many graphs of stopping times $T_n$) and dense. The main result is that whenever the increasing processes $I_{t\ge T_n}$ have absolutely continuous compensators (in which case the same property holds for any stopping time $T$ whose graph is contained in $B$), then the random set $B$ can be represented as the union of all the points of countably many independent standard Poisson processes (intuitively, a Poisson measure whose rate is $+\infty$ times Lebesgue measure). This may require, however, an innocuous enlargement of filtration. Another characterization of such random sets is roughly that they do not intersect previsible sets of zero Lebesgue measure. Note also an interesting example of a set optional w.r.t. two filtrations, but not w.r.t. their intersection

Keywords: Poisson point processes

Nature: Original

Retrieve article from Numdam

XX: 02, 28-29, LNM 1204 (1986)

Sur la représentation intégrale des martingales du processus de Poisson (Stochastic calculus, Point processes)

Dellacherie gave in 805 a proof by stochastic calculus of the previsible representation property for the Wiener and Poisson processes. A gap in this proof is filled in 928 for Brownian motion and here for Poisson processes

Keywords: Stochastic integrals, Previsible representation, Poisson processes

Nature: Correction

Retrieve article from Numdam

XLIII: 14, 341-349, LNM 2006 (2011)

The Lent Particle Method for Marked Point Processes (General theory of processes, Point processes)

Nature: Original