Decomposable Statistics and Random Placement of Particles over a Countable Set of Cells*
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In the paper, the scheme of independent particle allocation is considered. A connection is demonstrated between finite-dimensional distributions for the process of the number of particles assigned to the k-th cell and the conditional distribution of independent Poisson distributed random variables. Conditions are specified for the convergence of these distributions to finite-dimensional distributions of the Gaussian process. A certain scheme of dependent particle allocation on a countable set of cells is introduced and investigated.
KeywordsJoint Distribution Gaussian Process Conditional Distribution Null Vector Distinguishable Particle
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