Dirichlet Processes and an Intrinsic Characterization of Renormalized Intersection Local Times
نویسنده
چکیده
– We show that the nth order renormalized self-intersection local time γn(μ; t) for the symmetric stable process in R2, where the n-fold multiple points are weighted by an arbitrary measure μ, can be characterized as the continuous process of zero quadratic variation in the decomposition of a natural Dirichlet process. This Dirichlet process is the potential of a random measure associated with γn−1(μ; t). 2001 Éditions scientifiques et médicales Elsevier SAS RÉSUMÉ. – Lorsque les points multiples d’arche n sont changés par une mesure arbitraire μ, le temps local d’auto-intersection renormalisé γn(μ, t) du processus symétrique stable de R2 peutêtre caractérisé comme le processus de variation de quadratique nulle de la décomposition d’un processus de Dirichlet défini naturellement comme le potentiel d’une mesure aléatoire associée à γn−1(μ, t). 2001 Éditions scientifiques et médicales Elsevier SAS
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