The convolution equation of Choquet and Deny for probability measures on discrete semigroups
The critical case of the Cramer-Lundberg theorem on the asymptotic tail behavior of the maximum of a negative drift random walk.
The damped modified iterated Kalman filter for nonlinear discrete time systems
The determination of the spectral multiplicity of a stochastic process by RKHS method
The distribution of trees.
The distribution of eigenvalues of randomized permutation matrices
In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter ) by replacing the entries equal to one by more general non-vanishing complex random variables. For these ensembles, in contrast with more classical models as the Gaussian Unitary Ensemble, or the Circular Unitary Ensemble, the eigenvalues can be very explicitly computed by using the cycle structure of the permutations....
The distribution of non-commutative Rademacher series.
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 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 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 existence of a multiple spider martingale in the natural filtration of a certain diffusion in the plane
The Existence of Measurable Approximating Maximums.
The falling apart of the tagged fragment and the asymptotic disintegration of the brownian height fragmentation
We present a further analysis of the fragmentation at heights of the normalized brownian excursion. Specifically we study a representation for the mass of a tagged fragment in terms of a Doob transformation of the 1/2-stable subordinator and use it to study its jumps; this accounts for a description of how a typical fragment falls apart. These results carry over to the height fragmentation of the stable tree. Additionally, the sizes of the fragments in the brownian height fragmentation when it is...
The fractional mixed fractional brownian motion and fractional brownian sheet
We introduce the fractional mixed fractional Brownian motion and fractional Brownian sheet, and investigate the small ball behavior of its sup-norm statistic. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test. Finally, when we consider the sup-norm statistic, the necessity part is given by a second integral test.
The genealogy of self-similar fragmentations with negative index as a continuum random tree.
The generalized FGM distribution and its application to stereology of extremes
The generalized FGM distribution and related copulas are used as bivariate models for the distribution of spheroidal characteristics. It is shown that this model is suitable for the study of extremes of the 3D spheroidal particles observed in terms of their random planar sections.
The geometry of Brownian surfaces.
The Green formula and HP Spaces on trees.