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Invariant Random Measures on the Sphere

Theory of Probability & Its Applications, 1961
We consider a random measure $\mu $ on the spere S. One calls the measure $\mu $ invariant if ${\bf M}\mu (A)\mu (B) = {\bf M}\mu (gA)\overline {\mu (gB)} $ for every rotation g of the sphere.The following formula is proved: \[ \mu (A) = \sum\limits_{m = 0}^\infty {\sum\limits_{l = - m}^m {\xi _{m^l } \int_S {\overline {Y_m^l (x)} I_A (x)dx ...
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CONVERGENCE OF MEASURES AND RANDOM PROCESSES

Russian Mathematical Surveys, 1976
This article is concerned with general theorems on the so-called -convergence of measures on an arbitrary measurable space. This is defined as weak convergence of measures for a given class of functional. It seems that such a convergence concept is the most natural one in the study of limit theorems for random processes.
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Random Measures.

Journal of the American Statistical Association, 1987
K. B. Athreya, Olav Kallenberg
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Random Measures.

Journal of the American Statistical Association, 1978
M. R. Leadbetter, Olav Kallenberg
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Random quasi-periodic paths and quasi-periodic measures of stochastic differential equations

Journal of Differential Equations, 2021
Chunrong Feng, Huaizhong Zhao
exaly  

Compound Random Measures and their Use in Bayesian Non-Parametrics

Journal of the Royal Statistical Society Series B: Statistical Methodology, 2017
Fabrizio Leisen, Jim Griffin
exaly  

Distributional results for means of normalized random measures with independent increments

Annals of Statistics, 2003
Antonio Lijoi   +2 more
exaly  

A random set characterization of possibility measures

Information Sciences, 2004
Enrique Miranda   +2 more
exaly  

Random Measures

2015
Samuel N. Cohen, Robert J. Elliott
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Distributional properties of means of random probability measures

Statistics Surveys, 2009
Antonio Lijoi, Igor Pruenster
exaly  

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