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Displaying 21 –
40 of
270
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.
As said by Mareš and Mesiar, necessity of aggregation of complex real inputs appears almost in any field dealing with observed (measured) real quantities (see the citation below). For aggregation of probability distributions Sklar designed his copulas as early as in 1959. But surprisingly, since that time only a very few literature have appeared dealing with possibility to aggregate several different pairwise dependencies into one multivariate copula. In the present paper this problem is tackled...
The convergence rate of the expectation of the logarithm of the first return time , after being properly normalized, is investigated for ergodic Markov chains. I. Kontoyiannis showed that for any β > 0 we have a.s. for aperiodic cases and A. J. Wyner proved that for any ε >0 we have eventually, a.s., where is the probability of the initial n-block in x. In this paper we prove that converges to a constant depending only on the process where is the modified first return time with...
This article provides entropic inequalities for binomial-Poisson
distributions, derived from the two point space. They appear as local
inequalities of the M/M/∞ queue. They describe in particular the
exponential dissipation of Φ-entropies along this process. This simple
queueing process appears as a model of “constant curvature”, and plays for
the simple Poisson process the role played by the Ornstein-Uhlenbeck process
for Brownian Motion. Some of the inequalities are recovered by semi-group
...
The concept of -divergences was introduced by Csiszár in 1963 as measures of the ‘hardness’ of a testing problem depending on a convex real valued function on the interval . The choice of this parameter can be adjusted so as to match the needs for specific applications. The definition and some of the most basic properties of -divergences are given and the class of -divergences is presented. Ostrowski’s inequality and a Trapezoid inequality are utilized in order to prove bounds for an extension...
In this paper we establish an upper and a lower bound for the -divergence of two discrete random variables under likelihood ratio constraints in terms of the Kullback-Leibler distance. Some particular cases for Hellinger and triangular discimination, -distance and Rényi’s divergences, etc. are also considered.
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