On the volume of intersection of three independent Wiener sausages

van den Berg, M.

Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010) no. 2, pp. 313-337.

Soit K un ensemble compact, non-polaire dans ℝm (m≥3) et soit SKi(t)={Bi(s)+y: 0≤s≤t, y∈K} des saucisses de Wiener associées à des processus Browniens indépendants Bi, i=1, 2, 3 initialisés à 0. L'espérance des volumes de ⋂i=13SKi(t) par rapport à la mesure produit est obtenue en termes de la mesure d'équilibre de K lorsque t tend vers l'infini.

Let K be a compact, non-polar set in ℝm, m≥3 and let SKi(t)={Bi(s)+y: 0≤s≤t, y∈K} be Wiener sausages associated to independent brownian motions Bi, i=1, 2, 3 starting at 0. The expectation of volume of ⋂i=13SKi(t) with respect to product measure is obtained in terms of the equilibrium measure of K in the limit of large t.

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