On the product of probabilistic metric spaces
On the range of purely atomic probability measures
On the refined Heisenberg-Weyl type inequality.
On the relationship between Menger spaces and Wald spaces
On the Rényi theory of conditional probabilities
On the structure of intuitionistic algebras with relational probabilities.
Trillas ([1]) has defined a relational probability on an intuitionistic algebra and has given its basic properties. The main results of this paper are two. The first one says that a relational probability on a intuitionistic algebra defines a congruence such that the quotient is a Boolean algebra. The second one shows that relational probabilities are, in most cases, extensions of conditional probabilities on Boolean algebras.
Operations on distribution functions not derivable from operations on random variables
Operator valued probability theory.
Optimal solutions of multivariate coupling problems
Some necessary and some sufficient conditions are established for the explicit construction and characterization of optimal solutions of multivariate transportation (coupling) problems. The proofs are based on ideas from duality theory and nonconvex optimization theory. Applications are given to multivariate optimal coupling problems w.r.t. minimal -type metrics, where fairly explicit and complete characterizations of optimal transportation plans (couplings) are obtained. The results are of interest...
Optimality conditions for maximizers of the information divergence from an exponential family
The information divergence of a probability measure from an exponential family over a finite set is defined as infimum of the divergences of from subject to . All directional derivatives of the divergence from are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for to be a maximizer of the divergence from are presented, including new ones when is not projectable to .
Ordering probabilities on an ordered measurable space
Orlicz space - valued martingales
Philosophischer Versuch über die Wahrscheinlichkeiten [Book]
Posterior Probability on Finite Set
In [14] we formalized probability and probability distribution on a finite sample space. In this article first we propose a formalization of the class of finite sample spaces whose element’s probability distributions are equivalent with each other. Next, we formalize the probability measure of the class of sample spaces we have formalized above. Finally, we formalize the sampling and posterior probability.
Pravděpodobnost a posteriori. [I.]
Pravděpodobnost a posteriori. [II.]
Principes d'invariance pour la probabilité d'un dilaté de l'enveloppe convexe d'un échantillon
Probabilidades en cadena en los espacios de Hilbert. Aplicaciones físicas.
Probability in the alternative set theory
Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables
In this article we continue formalizing probability and randomness started in [13], where we formalized some theorems concerning the probability and real-valued random variables. In this paper we formalize the variance of a random variable and prove Chebyshev's inequality. Next we formalize the product probability measure on the Cartesian product of discrete spaces. In the final part of this article we define the algebra of real-valued random variables.