A Berry-Esseen theorem on semisimple Lie groups
A Central Limit Theorem for Approximate Martingale Arrays with Values in a Locally Compact Abelian Group.
A central limit theorem on the space of positive definite symmetric matrices
A central limit theorem is proved on the space of positive definite symmetric matrices. To do this, some natural analogs of the mean and dispersion on are defined and investigated. One uses a Taylor expansion of the spherical functions on .
A characterization of Gaussian measures on Banach spaces
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 weak convergence of convolution powers
A continuous mapping theorem for the argmin-set functional with applications to convex stochastic processes
For lower-semicontinuous and convex stochastic processes and nonnegative random variables we investigate the pertaining random sets of all -approximating minimizers of . It is shown that, if the finite dimensional distributions of the converge to some and if the converge in probability to some constant , then the converge in distribution to in the hyperspace of Vietoris. As a simple corollary we obtain an extension of several argmin-theorems in the literature. In particular, in...
A convergence of fuzzy random variables
In this paper, a general convergence theorem of fuzzy random variables is considered. Using this result, we can easily prove the recent result of Joo et al, which gives generalization of a strong law of large numbers for sums of stationary and ergodic processes to the case of fuzzy random variables. We also generalize the recent result of Kim, which is a strong law of large numbers for sums of levelwise independent and levelwise identically distributed fuzzy random variables.
A Decomposition Theorem for Additive Set-Functions, with Applications to Pettis Integrals and Ergodic Means.
A Gaussian bound for convolutions of functions on locally compact groups
We give new and general sufficient conditions for a Gaussian upper bound on the convolutions of a suitable sequence K₁, K₂, K₃, ... of complex-valued functions on a unimodular, compactly generated locally compact group. As applications, we obtain Gaussian bounds for convolutions of suitable probability densities, and for convolutions of small perturbations of densities.
A general bounded continuous moment problem and its sets of uniqueness
A general Choquet–Deny theorem for nilpotent groups
A general purity law for convolution semigroups with discrete Levy measure.
A general version of delta theorem
A generalization of the global limit theorems of R. P. Agnew.
A generalized Chacon's inequality and order convergence of processes
A geometry on the space of probabilities (II). Projective spaces and exponential families.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...
A Green's Function for Non-Homogegeous Random Walks on Free Products.
A Law of the Iterated Logarithm for a Class of Polynomial Hypergroups.