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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), 2017
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.
LEAO Jr., D., FRAGOSO, M., RUFFINO, P.
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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
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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
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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
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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
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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
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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.
Landers, D., Rogge, L.
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Determinants of hypertension among Bhutanese adults: evidence from a national WHO STEPS survey [PDF]

Scientific Reports
Hypertension is an emerging public health problem in Bhutan due to epidemiological and nutritional transitions in the last two decades. This study aimed to quantify risk factors of hypertension in Bhutan using nationally representative data.
Kuenzang Chhezom, Kinley Wangdi
doaj   +2 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
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