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4 matches found
III: 14, 175-189, LNM 88 (1969)
MEYER, Paul-André
Processus à accroissements indépendants et positifs (Markov processes, Independent increments)
This is an exposition of the theory of subordinators (Lévy processes with increasing paths), aiming at presenting Chung's conjecture that a certain identity known to hold a.e. actually holds everywhere, also equivalent to the fact that single points are polar sets for subordinators without drift
Comment: The conjecture was proved by Kesten (see 503) who actually knew of the problem through this talk. See also 502
Keywords: Subordinators, Polar sets
Nature: Exposition
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V: 02, 17-20, LNM 191 (1971)
ASSOUAD, Patrice
Démonstration de la ``Conjecture de Chung'' par Carleson (Markov processes, Independent increments)
Chung conjectured that singletons are polar sets for driftless subordinators. This paper gives Carleson's (unpublished) analytic proof of it
Comment: See Chung, C. R. Acad. Sci. , 260, 1965, p.4665. For the statement of the problem see Meyer 314. For Kesten's earlier (contrary to a statement in the paper!) probabilistic proof see Bretagnolle 503. See also Séminaire Bourbaki 21th year, 361, June 1969
Keywords: Subordinators, Polar sets
Nature: Exposition
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V: 03, 21-36, LNM 191 (1971)
Résultats de Kesten sur les processus à accroissements indépendants (Markov processes, Independent increments)
The question is to find all Lévy processes for which single points are polar. Kesten's answer (Mem. Amer. Math. Soc., 93, 1969) is almost complete and in particular proves Chung's conjecture. The proofs in this paper have been considerably reworked
Comment: See also 502 in the same volume
Keywords: Subordinators, Polar sets
Nature: Exposition, Original additions
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V: 15, 147-169, LNM 191 (1971)
Ensembles régénératifs, temps locaux et subordinateurs (General theory of processes, Renewal theory)
New approach to the theory of regenerative sets (Kingman; Krylov-Yushkevic 1965, Hoffmann-Jørgensen, Math. Scand., 24, 1969), including a general definition of local time of a random set
Comment: See Meyer 412, Morando-Maisonneuve 413, later work of Maisonneuve in 813 and later
Keywords: Local times, Subordinators, Renewal theory
Nature: Original
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