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Quelques proprietes du mouvement Brownien dans un cone

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  • Biane, Philippe

Abstract

On montre plusieurs résultat généraux sur le comportement du mouvement Brownien dans un cône, conditionné à ne pas toucher le bord du cône. En particulier si le cône est un simplexe, on calcule la loi du minimum futur (pour l'ordre associé au cône) de ce processus. On applique ces résultats au cas d'un cône d'ouverture dans 2. Dans ce cas on a un analogue du théorème de Pitman: si on considère le mouvement Brownien conditionné à ne pas toucher le bord, auquel on retranche trois fois son minimum futur, la composante de ce processus orthogonale à l'axe du cône est un mouvement Brownien.

Suggested Citation

  • Biane, Philippe, 1994. "Quelques proprietes du mouvement Brownien dans un cone," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 233-240, October.
    • Handle: RePEc:eee:spapps:v:53:y:1994:i:2:p:233-240
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