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A characterization of harmonic measure and Markov processes whose hitting distributions are preserved by rotations translations and dilatations

Bernt Oksendal, Daniel W. Stroock (1982)

Annales de l'institut Fourier

The exit distribution for open sets of a path-continuous, strong Markov process in R n 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,...

A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Yuri Bakhtin, Matilde Martánez (2008)

Annales de l'I.H.P. Probabilités et statistiques

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 T 1 of which is invariant under both the geodesic and the horocycle flows.

A characterization of harmonic sections and a Liouville theorem

Simão Stelmastchuk (2012)

Archivum Mathematicum

Let P ( M , G ) be a principal fiber bundle and E ( M , N , G , P ) an associated fiber bundle. Our interest is to study the harmonic sections of the projection π E of E into M . Our first purpose is give a characterization of harmonic sections of M into E regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of π E .

A characterization of probability measures by f-moments

K. Urbanik (1996)

Studia Mathematica

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 ʃ 0 ƒ ( x ) μ * n ( d x ) (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 ( - 1 ) n ƒ ( n + 1 ) ( x ) is completely monotone for some nonnegative integer n. The purpose of this paper...

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