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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
SOME SMALL DEVIATION THEOREMS FOR ARBITRARY RANDOM FIELDS WITH RESPECT TO BINOMIAL DISTRIBUTIONS INDEXED BY AN INFINITE TREE ON GENERALIZED RANDOM SELECTION SYSTEMS
Journal of applied mathematics & informatics. 2015. Sep, 33(5_6): 517-530
  • Received : December 12, 2014
  • Published : September 30, 2015
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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.
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