A note on the exact expected length of the th part of a random partition.
A note on the existence of Gibbs marked point processes with applications in stochastic geometry
This paper generalizes a recent existence result for infinite-volume marked Gibbs point processes. We try to use the existence theorem for two models from stochastic geometry. First, we show the existence of Gibbs facet processes in with repulsive interactions. We also prove that the finite-volume Gibbs facet processes with attractive interactions need not exist. Afterwards, we study Gibbs-Laguerre tessellations of . The mentioned existence result cannot be used, since one of its assumptions...
A note on the exponential convergence rate for products of sums
A note on the functional law of the iterated logarithm for Lévy's area process
By using large deviation techniques, we prove a Strassen type law of the iterated logarithm, in Hölder norm, for Lévy's area process.
A note on the Glauber dynamics for sampling independent sets.
A note on the good lambda inequalities
A note on the interval-valued marginal problem and its maximum entropy solution
This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of the paper.
A note on the invariance principle of the product of sums of random variables.
A note on the k-th distance random variables
A note on the L1-convergence of a superadditive bisexual Galton-Watson process.
A note on the martingale central limit theorem
A note on the martingale inequality.
A Note on the Men'shov-Rademacher Inequality
We improve the constants in the Men’shov-Rademacher inequality by showing that for n ≥ 64, for all orthogonal random variables X₁,..., Xₙ such that .
A note on the optimal replacement policy
A system with a single activated unit, which can be in a finite number of states, is considered. Inspections of the system are carried out at discrete time instants. It is possible to replace it by a new one at these moments. The user of the system, by setting down conditions of replacements, wants to maximize his gain, which does not include the rest value of units. On a numerical example it is shown that the frequency of replacements of the unit need not be the greater the longer is the period...
A note on the Poisson disorder problem
A Note on the Product of Random Elements of a Semigroup.
A note on the rate of complete convergence for maximums of partial sums for moving average processes in Rademacher type Banach spaces.
A note on the rate of complete convergence for weighted sums of arrays of Banach space valued random elements.
A note on the Runge-Kutta method for stochastic differential equations
In the paper the convergence of a mixed Runge--Kutta method of the first and second orders to a strong solution of the Ito stochastic differential equation is studied under a monotonicity condition.
A note on the strong consistency of least squares estimates
The strong consistency of least squares estimates in multiples regression models with i.i.d. errors is obtained under assumptions on the design matrix and moment restrictions on the errors.