Some Small Deviation Theorems for the Sequence of Binary Random Truncated Functions on a Homogeneous Tree


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New Zealand Journal of Mathematics

Vol. 42, (2012), Pages 91-106

Kangkang Wang

School of Mathematics and Physics,

Jiangsu University of Science and Technology,

Zhenjiang 212003,


Weicai Peng

Department of Mathematics,

Chaohu University,

Chaohu 238000,


Abstract In this paper, a class of small-deviation theorems for the sequence of random truncated functions on arbitrary random field indexed by the homogeneous tree are established by utilizing asymptotic logarithmic likelihood ratio on the homogeneous tree. As corollaries, some strong limit theorems for the arbitrary random field on the homogeneous tree are obtained.

Keywords small deviation theorem, the homogeneous tree, arbitrary random field, truncated function sequence, asymptotic logarithmic likelihood ratio.

Classification (MSC2000) 60F15.

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