A Class of Strong Limit Theorems for Random Field with Geometric Distributions Indexed by a Homogeneous Tree

Kang Kang Wang

Abstract

In this paper, we establish some strong limit theorem for the random field which
obeys the geometric distributions indexed by the homogeneous tree by constructing the
consistent distribution and a nonnegative martingale with pure analytical methods.
As corollaries, a limit theorem for the sequence of random variables with the geometric
distributions is extended.60F15