Metrics on states from actions of compact groups.
Mixing times for Markov chains on wreath products and related homogeneous spaces.
Moderate Growth and Random Walk on Finite Groups.
Moment functions and laws of large numbers on hypergroups.
Moments of probability measures on a group.
Multivariate tail equivalence of distributions in extreme value theory
New metrics for weak convergence of distribution functions.
Sibley and Sempi have constructed metrics on the space of probability distribution functions with the property that weak convergence of a sequence is equivalent to metric convergence. Sibley's work is a modification of Levy's metric, but Sempi's construction is of a different sort. Here we construct a family of metrics having the same convergence properties as Sibley's and Sempi's but which does not appear to be related to theirs in any simple way. Some instances are brought out in which the metrics...
Nonlinear diffusion with jumps
Norm convergence of random walks on compact hypergroups.
On a distribution problem in finite sets
On a theorem of Kłosowska about generalised convolutions
On approximation of copulas.
On asymptotic behaviour of empirical processes
On continuous convergence and epi-convergence of random functions. Part I: Theory and relations
Continuous convergence and epi-convergence of sequences of random functions are crucial assumptions if mathematical programming problems are approximated on the basis of estimates or via sampling. The paper investigates “almost surely” and “in probability” versions of these convergence notions in more detail. Part I of the paper presents definitions and theoretical results and Part II is focused on sufficient conditions which apply to many models for statistical estimation and stochastic optimization....
On continuous convergence and epi-convergence of random functions. Part II: Sufficient conditions and applications
Part II of the paper aims at providing conditions which may serve as a bridge between existing stability assertions and asymptotic results in probability theory and statistics. Special emphasis is put on functions that are expectations with respect to random probability measures. Discontinuous integrands are also taken into account. The results are illustrated applying them to functions that represent probabilities.
On convergence of infinitely divisible distributions in a Hilbert space
On Ito-Nisio type theorems for DS-groups.
On non-ergodic versions of limit theorems
The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds.
On the Argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies
Let be the collection of all -optimal solutions for a stochastic process with locally bounded trajectories defined on a topological space. For sequences of such stochastic processes and of nonnegative random variables we give sufficient conditions for the (closed) random sets to converge in distribution with respect to the Fell-topology and to the coarser Missing-topology.
On the convolution of a probability measure.