Minkowski sums and Brownian exit times
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 1, p. 37-47

If C is a domain in R n , the Brownian exit time of C is denoted by T C . Given domains C and D in R n this paper gives an upper bound of the distribution function of T C+D when the distribution functions of T C and T D are known. The bound is sharp if C and D are parallel affine half-spaces. The paper also exhibits an extension of the Ehrhard inequality

Si C est un domaine de R n , le temps de sortie brownien de C est noté T C . Donnant domaines C et D de R n cet article montre une borne supérieure pour la fonction de répartition de T C+D quand les fonctions de répartition de T C et T D sont connues. En plus l’article exhibe une généralisation de l’inégalité d’Ehrhard.

@article{AFST_2007_6_16_1_37_0,
     author = {Borell, Christer},
     title = {Minkowski sums and Brownian exit times},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 16},
     number = {1},
     year = {2007},
     pages = {37-47},
     doi = {10.5802/afst.1137},
     zbl = {1148.60062},
     mrnumber = {2325590},
     zbl = {pre05247237},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2007_6_16_1_37_0}
}

Borell, Christer. Minkowski sums and Brownian exit times. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 1, pp. 37-47. doi : 10.5802/afst.1137. http://www.numdam.org/item/AFST_2007_6_16_1_37_0/

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