Discrete marginal problem for complex measures
František Matúš (1988)
Kybernetika
Antoine Ehrhard (1986)
Annales de l'I.H.P. Probabilités et statistiques
Theodore P. Hill (1985)
Mathematische Zeitschrift
S. Mitrović (1984)
Matematički Vesnik
Patrizia Berti, Luca Pratelli, Pietro Rigo, Fabio Spizzichino (2015)
Dependence Modeling
Let (X,A) and (Y,B) be measurable spaces. Supposewe are given a probability α on A, a probability β on B and a probability μ on the product σ-field A ⊗ B. Is there a probability ν on A⊗B, with marginals α and β, such that ν ≪ μ or ν ~ μ ? Such a ν, provided it exists, may be useful with regard to equivalent martingale measures and mass transportation. Various conditions for the existence of ν are provided, distinguishing ν ≪ μ from ν ~ μ.
Thierry de La Rue (1993)
Séminaire de probabilités de Strasbourg
Lionel Thibault (1981)
Annales de l'I.H.P. Probabilités et statistiques
Friedrich Liese (1987)
Kybernetika
Heinrich V. Weizsäcker (1983)
Annales de l'I.H.P. Probabilités et statistiques
Tommy Norberg (1989)
Mathematica Scandinavica
Evans, Steven N., Lidman, Tye (2007)
Electronic Journal of Probability [electronic only]
Friedrich Liese (1987)
Kybernetika
Daniel Hlubinka (2002)
Commentationes Mathematicae Universitatis Carolinae
Having Polish spaces , and we shall discuss the existence of an -valued random vector such that its conditional distributions satisfy or for some maps , or multifunction respectively. The problem is equivalent to the existence of universally measurable Markov kernel defined implicitly by or respectively. In the paper we shall provide sufficient conditions for the existence of the desired Markov kernel. We shall discuss some special solutions of the - or -problem and illustrate...
Radko Mesiar (1982)
Mathematica Slovaca
Jan Šindelář, Pavel Boček (2002)
Kybernetika
Classes of strings (infinite sequences resp.) with a specific flow of Kolmogorov complexity are introduced. Namely, lower bounds of Kolmogorov complexity are prescribed to strings (initial segments of infinite sequences resp.) of specified lengths. Dependence of probabilities of the classes on lower bounds of Kolmogorov complexity is the main theme of the paper. Conditions are found under which the probabilities of the classes of the strings are close to one. Similarly, conditions are derived under...
Jan Šindelář, Pavel Boček (2002)
Kybernetika
An attempt to formalize heuristic concepts like strings (sequences resp.) “typical” for a probability measure is stated in the paper. Both generating and testing of such strings is considered. Kolmogorov complexity theory is used as a tool. Classes of strings “typical” for a given probability measure are introduced. It is shown that no pseudorandom generator can produce long strings from the classes. The time complexity of pseudorandom generators with oracles capable to recognize “typical” strings...
Radko Mesiar (1985)
Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
Franck Barthe (2001)
Annales de la Faculté des sciences de Toulouse : Mathématiques
Michael M. Erlihson, Boris L. Granovsky (2008)
Annales de l'I.H.P. Probabilités et statistiques
We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ak∼Ckp−1, k→∞, p>0, where C is a positive constant. The measures considered are associated with the generalized Maxwell–Boltzmann models in statistical mechanics, reversible coagulation–fragmentation processes and combinatorial structures, known as assemblies. We prove a central limit theorem for fluctuations of a properly scaled partition...
Roman Frič (2002)
Czechoslovak Mathematical Journal
We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean -algebra) can be uniquely extended to a sequentially continuous measure on the generated Łukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on Łukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields...