A Characteristic Property for Maxima of Random Variables with Trivial Analogue When Sums are Concerned
The exit distribution for open sets of a path-continuous, strong Markov process in is characterized as a weak star limit of successive spherical sweepings of measures, starting with the unit point mass. Then this is used to prove that two path-continuous strong Markov processes with identical exit distributions from balls when starting form the center, have identical exit distributions from all opens sets, provided they both exit a.s. from bounded sets. This implies that the only path-continuous,...
denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on is harmonic if and only if it is the projection of a measure on the unit tangent bundle of which is invariant under both the geodesic and the horocycle flows.
Let be a principal fiber bundle and an associated fiber bundle. Our interest is to study the harmonic sections of the projection of into . Our first purpose is give a characterization of harmonic sections of into regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of .
Given a real-valued continuous function ƒ on the half-line [0,∞) we denote by P*(ƒ) the set of all probability measures μ on [0,∞) with finite ƒ-moments (n = 1,2...). A function ƒ is said to have the identification propertyif probability measures from P*(ƒ) are uniquely determined by their ƒ-moments. A function ƒ is said to be a Bernstein function if it is infinitely differentiable on the open half-line (0,∞) and is completely monotone for some nonnegative integer n. The purpose of this paper...
A characteriyation of the Gamma distribution in terms of the -th conditional moment presented in this paper extends the result of Shunji Osaki and Xin-xiang Li (1988).