Si est un domaine de R le temps de sortie brownien de est noté . Donnant domaines et de R cet article montre une borne supérieure pour la fonction de répartition de quand les fonctions de répartition de et sont connues. En plus l’article exhibe une généralisation de l’inégalité d’Ehrhard.
If is a domain in R the Brownian exit time of is denoted by Given domains and in R this paper gives an upper bound of the distribution function of when the distribution functions of and are known. The bound is sharp if and are parallel affine half-spaces. The paper also exhibits an extension of the Ehrhard inequality
@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}, pages = {37--47}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, volume = {Ser. 6, 16}, number = {1}, year = {2007}, doi = {10.5802/afst.1137}, zbl = {1148.60062}, mrnumber = {2325590}, language = {en}, url = {archive.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, Série 6, Tome 16 (2007) no. 1, pp. 37-47. doi : 10.5802/afst.1137. http://archive.numdam.org/item/AFST_2007_6_16_1_37_0/
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