On the volume of intersection of three independent Wiener sausages
Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 2, p. 313-337

Let K be a compact, non-polar set in ℝm, m≥3 and let SKi(t)={Bi(s)+y: 0≤st, yK} 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.

Soit K un ensemble compact, non-polaire dans ℝm (m≥3) et soit SKi(t)={Bi(s)+y: 0≤st, yK} 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.

DOI : https://doi.org/10.1214/09-AIHP316
Classification:  35K20,  60J65,  60J45
Keywords: Wiener sausage, equilibrium measure
@article{AIHPB_2010__46_2_313_0,
     author = {Van den Berg, M.},
     title = {On the volume of intersection of three independent Wiener sausages},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {46},
     number = {2},
     year = {2010},
     pages = {313-337},
     doi = {10.1214/09-AIHP316},
     zbl = {1201.35108},
     mrnumber = {2667701},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2010__46_2_313_0}
}
van den Berg, M. On the volume of intersection of three independent Wiener sausages. Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 2, pp. 313-337. doi : 10.1214/09-AIHP316. http://www.numdam.org/item/AIHPB_2010__46_2_313_0/

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