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Propriétés de martingales, explosion et représentation de Lévy--Khintchine d'une classe de processus de branchement à valeurs mesures

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  • El Karoui, Nicole
  • Roelly, Sylvie

Abstract

Résumé On étudie par des méthodes de type calcul stochastique les propriétés de martingales d'une classe très générale de processus de branchement à valeurs mesures. Leurs caractéristiques locales et temps d'explosion sont explicités en fonction de la forme de leur cumulant. Enfin, grâce à l'infinie divisibilité de ces processus, on obtient une représentation de Lévy-Khintchine sur l'espace des trajectoires qui permet d'interpréter leurs mesures canoniques comme des lois d'entrées.

Suggested Citation

  • El Karoui, Nicole & Roelly, Sylvie, 1991. "Propriétés de martingales, explosion et représentation de Lévy--Khintchine d'une classe de processus de branchement à valeurs mesures," Stochastic Processes and their Applications, Elsevier, vol. 38(2), pages 239-266, August.
    • Handle: RePEc:eee:spapps:v:38:y:1991:i:2:p:239-266
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    Cited by:

    1. Li Wang, 2018. "Central Limit Theorems for Supercritical Superprocesses with Immigration," Journal of Theoretical Probability, Springer, vol. 31(2), pages 984-1012, June.
    2. Mandler, Christian & Overbeck, Ludger, 2022. "A functional Itō-formula for Dawson–Watanabe superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 202-228.
    3. He, Hui, 2009. "Discontinuous superprocesses with dependent spatial motion," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 130-166, January.
    4. Kyprianou, A.E. & Ren, Y.-X., 2012. "Backbone decomposition for continuous-state branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 139-144.
    5. Li, Zenghu & Zhang, Mei, 2006. "Fluctuation limit theorems of immigration superprocesses with small branching," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 401-411, February.
    6. Dawson, Donald A. & Hochberg, Kenneth J. & Vinogradov, Vladimir, 1996. "High-density limits of hierarchically structured branching-diffusing populations," Stochastic Processes and their Applications, Elsevier, vol. 62(2), pages 191-222, July.
    7. Leduc, Guillaume, 2006. "Martingale problem for superprocesses with non-classical branching functional," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1468-1495, October.
    8. Ren, Yan-Xia & Song, Renming & Zhang, Rui, 2015. "Central limit theorems for supercritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 428-457.

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