Results 1 to 10 of about 245,498 (265)
Large Deviations of Continuous Regular Conditional Probabilities [PDF]
Journal of Theoretical Probability, 2016 We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a sequence of probability measures on the product space that satisfies a large deviation principle, we present necessary
W. van Zuijlen
core +7 more sources
Regular conditional probability, disintegration of probability and Radon spaces [PDF]
Proyecciones (Antofagasta), 2009 We establish equivalence of several regular conditional probability properties and Radon space. In addition, we introduce the universally measurable disintegration concept and prove an existence result.
D. A. Leão +2 more
openalex +3 more sources
Perfect Probability Measures and Regular Conditional Probabilities [PDF]
The Annals of Mathematical Statistics, 1966 In an attempt to refine the axiomatic model of a probability space introduced by Kolmogorov [11], Gnendenko and Kolmogorov [5] introduced the concept of a perfect probability measure. The desirability of some sort of refinement has been pointed out by several well known examples [2], [3], [8], which display a certain amount of pathology inherent in ...
Robert H. Rodine
openalex +3 more sources
Existence of Independent Complements in Regular Conditional Probability Spaces [PDF]
The Annals of Probability, 1979 Let $(X, \mathscr{A}, P)$ be a probability space and $\mathscr{B}$ a sub-$\sigma$-algebra of $\mathscr{A}$. Some results on regular conditional probabilities given $\mathscr{B}$ are proved. Using these, when $\mathscr{A}$ is separable and $\mathscr{B}$ is a countably generated sub-$\sigma$-algebra of $\mathscr{A}$ such that there is a regular ...
D. Ramachandran
openalex +4 more sources
A Note on Regular Conditional Probabilities in Doob's Sense [PDF]
The Annals of Probability, 1981 It is pointed out that an example due to J. Pachl shows the nonexistence of regular conditional probabilities in Doob's sense when the underlying space is a perfect probability space. This answers a question of Sazonov.
D. Ramachandran
openalex +4 more sources
On the existence of regular conditional probabilities [PDF]
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1969 Let (X, A, P) be a measure space with P(X)=1 and ∇ a sub-σ-algebra. It is well known (see e.g. Doob, p. 624) that even if A is separable, a regular conditional probability (r.c.p.) on A, given ∇, does not always exist. All theorems assuring the existence of a r.c.p.
J. Pfanzagl
openalex +2 more sources
Existence of compatible families of proper regular conditional probabilities [PDF]
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1981 Let (Ω, ℱ, μ) be a perfect probability space with ℱ countably generated, and let IB be a family of sub-σ-fields of ℱ. Under a countability condition on the family IB, I show that there exists a family {π∇}∇∈IB of regular conditional probabilities which are everywhere compatible. Under a more stringent condition on IB, I show that the π∇ can furthermore
Alan D. Sokal
+4 more sources
The Existence of Regular Conditional Probabilities: Necessary and Sufficient Conditions
The Annals of Probability, 1985 Let (Y,\({\mathcal T},\mu)\) be a probability space, (X,\({\mathcal S})\) a measurable space and \(\nu: Y\times {\mathcal S}\to [0,1]\) a kernel. A probability space (X,\({\mathcal S},\mu)\) has the product regular conditional probability property (rcpp) if for any probability space (X\(\times Y,{\mathcal S}\times {\mathcal T},\lambda)\) for which ...
Arnold M. Faden
openalex +3 more sources
Existence of sufficient regular conditional probabilities
Manuscripta Mathematica, 1972 If a -field is sufficient for a family of probability measures defined on a -field then there exist regular determinations of the conditional probability of P, given , which are independent of the special measure , provided that is -regular.
Dieter Landers, Lothar Rogge
openalex +2 more sources
On regular conditional probabilities [PDF]
Czechoslovak Mathematical Journal, 1959 Miloslav Jiřina
openalex +3 more sources