A characterization of Gaussian measures
A characterization of Gaussian measures on Banach spaces
A characterization of Gaussian processes that are Markovian
A characterization of harmonic measure and Markov processes whose hitting distributions are preserved by rotations translations and dilatations
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,...
A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces
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.
A characterization of harmonic sections and a Liouville theorem
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 .
A characterization of Markov solutions for stochastic differential equations with jumps
A characterization of probability measures by f-moments
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 characterization of random approximations.
A Characterization of the Banach Spaces of Type p by Lévy Measures.
A characterization of the domain of attraction of a normal distribution in a Hilbert space
A Characterization of the Expontential Distribution
A characterization of the gamma distribution in terms of conditional moment
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).
A characterization of the set of fixed points of the quicksort transformation.
A characterization of the weak convergence of convolution powers
A Characterization of Uniform Distribution
Is the Lebesgue measure on [0,1]² a unique product measure on [0,1]² which is transformed again into a product measure on [0,1]² by the mapping ψ(x,y) = (x,(x+y)mod 1))? Here a somewhat stronger version of this problem in a probabilistic framework is answered. It is shown that for independent and identically distributed random variables X and Y constancy of the conditional expectations of X+Y-I(X+Y > 1) and its square given X identifies uniform distribution either absolutely continuous or discrete....
A characterization of α-convolutions
A Characterization using the Conditional Variance.
A Ciesielski–Taylor type identity for positive self-similar Markov processes
The aim of this note is to give a straightforward proof of a general version of the Ciesielski–Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski–Taylor identities within the latter class. The approach makes use of three fundamental features. Firstly, a new transformation which maps a subset of the family of Laplace exponents of spectrally negative Lévy processes into itself. Secondly, some classical features...
A clark-ocone formula in UMD Banach spaces.