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SOME SMALL DEVIATION THEOREMS FOR ARBITRARY RANDOM FIELDS WITH RESPECT TO BINOMIAL DISTRIBUTIONS INDEXED BY AN INFINITE TREE ON GENERALIZED RANDOM SELECTION SYSTEMS
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 Title & Authors
SOME SMALL DEVIATION THEOREMS FOR ARBITRARY RANDOM FIELDS WITH RESPECT TO BINOMIAL DISTRIBUTIONS INDEXED BY AN INFINITE TREE ON GENERALIZED RANDOM SELECTION SYSTEMS
LI, FANG; WANG, KANGKANG;
 
 Abstract
In this paper, we establish a class of strong limit theorems, represented by inequalities, for the arbitrary random field with respect to the product binomial distributions indexed by the infinite tree on the generalized random selection system by constructing the consistent distri-bution and a nonnegative martingale with pure analytical methods. As corollaries, some limit properties for the Markov chain field with respect to the binomial distributions indexed by the infinite tree on the generalized random selection system are studied.
 Keywords
the infinite tree;generalized random selection system;random field;the binomial distribution;nonnegative martingale;small deviation theorem;
 Language
English
 Cited by
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