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

### From NZJM

**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,

China

**Weicai Peng**

Department of Mathematics,

Chaohu University,

Chaohu 238000,

China

**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.