Minkowski sums and Brownian exit times

Journal article, 2007

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.