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 timesNature: 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 theoryNature: Original Retrieve article from Numdam
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 processesNature: Original Retrieve article from Numdam
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 processesNature: Correction Retrieve article from Numdam
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
