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A note on the existence of Gibbs marked point processes with applications in stochastic geometry

Martina Petráková (2023)

Kybernetika

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 ℝ d 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 ℝ 2 . The mentioned existence result cannot be used, since one of its assumptions...

A note on the interval-valued marginal problem and its maximum entropy solution

Jiřina Vejnarová (1998)

Kybernetika

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 Men'shov-Rademacher Inequality

Witold Bednorz (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

We improve the constants in the Men’shov-Rademacher inequality by showing that for n ≥ 64, E ( s u p 1 ≤ k ≤ n | ∑ i = 1 k X i | ² ≤ 0 . 11 ( 6 . 20 + l o g ₂ n ) ² for all orthogonal random variables X₁,..., Xₙ such that ∑ k = 1 n E | X k | ² = 1 .

A note on the optimal replacement policy

Antonín Lešanovský, Petr Pěnička (1983)

Aplikace matematiky

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 strong consistency of least squares estimates

Joǎo Lita da Silva (2009)

Discussiones Mathematicae Probability and Statistics

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.

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