Enveloppes convexes des processus gaussiens
Estimates of some probabilities in multidimensional convex records
Convex records in Euclidean space are considered. We provide both lower and upper bounds on the probability that in a sequence of random vectors ,..., there are exactly k records.
Estimating an even spherical measure from its sine transform
To reconstruct an even Borel measure on the unit sphere from finitely many values of its sine transform a least square estimator is proposed. Applying results by Gardner, Kiderlen and Milanfar we estimate its rate of convergence and prove strong consistency. We close this paper by giving an estimator for the directional distribution of certain three-dimensional stationary Poisson processes of convex cylinders which have applications in material science.
Estimation of intersection intensity in a Poisson process of segments
The minimum variance unbiased estimator of the intensity of intersections is found for stationary Poisson process of segments with parameterized distribution of primary grain with known and unknown parameters. The minimum variance unbiased estimators are compared with commonly used estimators.
Existence et régularité höldérienne des fonctions de bosses
We discuss the almost sure existence of random functions that can be written as sums of elementary pulses. We then estimate their uniform Hölder regularity by applying some results on coverings by random intervals.
Existence theorems for measures on continous posets, with applications to random set theory.
Expectation and variance of the volume covered by a large number of independent random sets
Expectation of Random Polytopes.
Functionals of spatial point processes having a density with respect to the Poisson process
-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Itô chaos expansion. In the second half we obtain more explicit results for a system of -statistics of some parametric models in stochastic geometry. In the logarithmic form functionals are connected to Gibbs models. There is an inequality between moments of Poisson...
Gaussian approximation for functionals of Gibbs particle processes
In the paper asymptotic properties of functionals of stationary Gibbs particle processes are derived. Two known techniques from the point process theory in the Euclidean space are extended to the space of compact sets on equipped with the Hausdorff metric. First, conditions for the existence of the stationary Gibbs point process with given conditional intensity have been simplified recently. Secondly, the Malliavin-Stein method was applied to the estimation of Wasserstein distance between the...
Gaussian behaviour and average of marginals for convex bodies.
Gaussian limits for random geometric measures.
Generalization of a formula of C. Buchta about the convex hull of random points.
Geometric probabilities for convex bodies of large revolution in the Euclidean space . II.
Geometric probabilities for non convex lattices. II
We solve problems of Buffon type for a lattice with elementary tile a nonconvex polygon, using as test bodies a line sigment and a circle.
Geometrical probabilities for convex test bodies.
Geometrické pravděpodobnosti [Book]
Grundgleichungen der Stereologie I
Grundgleichungen der Stereologie II.
Hausdorff dimension of affine random covering sets in torus
We calculate the almost sure Hausdorff dimension of the random covering set in -dimensional torus , where the sets are parallelepipeds, or more generally, linear images of a set with nonempty interior, and are independent and uniformly distributed random points. The dimension formula, derived from the singular values of the linear mappings, holds provided that the sequences of the singular values are decreasing.