The distribution of non-commutative Rademacher series.
The distribution of the discrete tree length on a line
The distribution of the interval between events of a Cox process with shot noise intensity.
The distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous planar anisotropic STIT Tessellations
A result about the distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous and isotropic random tessellations stable under iteration (STIT tessellations) is extended to the anisotropic case using recent findings from Schreiber/Thäle, Typical geometry, second-order properties and central limit theory for iteration stable tessellations, arXiv:1001.0990 [math.PR] (2010). Moreover a new expression for the values of this probability distribution is presented...
The distribution of the values of a random function in the unit disk
The distribution of time spent by a standard excursion above a given level, with applications to ring polymers near a discontinuity in potential.
The distribution of unbounded random sets and the multivalued strong law of large numbers in nonreflexive Banach spaces.
The domain of attraction of a non-Gaussian stable distribution in a Hilbert space
The domain of attraction of non-Gaussian stable distribution in a Hilbert space, II
The Donsker delta function of a Lévy process with application to chaos expansion of local time
The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces
We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.
The dyadic fractional diffusion kernel as a central limit
We obtain the fundamental solution kernel of dyadic diffusions in as a central limit of dyadic mollification of iterations of stable Markov kernels. The main tool is provided by the substitution of classical Fourier analysis by Haar wavelet analysis.
The dynamics of -quantum spaces
The dynamics of mutation-selection algorithms with large population sizes
The Dyson Brownian Minor Process
Consider an Hermitean matrix valued stochastic process where the elements evolve according to Ornstein-Uhlenbeck processes. It is well known that the eigenvalues perform a so called Dyson Brownian motion, that is they behave as Ornstein-Uhlenbeck processes conditioned never to intersect.In this paper we study not only the eigenvalues of the full matrix, but also the eigenvalues of all the principal minors. That is, the eigenvalues of the minors in the upper left corner of . Projecting this...
The effect of random scale changes on limits of infinitesimal systems.
The efficiency of variance reduction in manufacturing and service systems: the comparison of the control variates and stratified sampling.
The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in
Considering the centered empirical distribution function Fn-F as a variable in , we derive non asymptotic upper bounds for the deviation of the -norms of Fn-F as well as central limit theorems for the empirical process indexed by the elements of generalized Sobolev balls. These results are valid for a large class of dependent sequences, including non-mixing processes and some dynamical systems.
The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile
The empirical TES methodology: Modeling empirical time series.