Abstract
Probability theory is a branch of mathematics dealing with chance Phenomena and has clearly discernible links with the real world. It is the framework foundations of many applying subjects, such as Information theory, Mathematics Risk theory and Insurance theory for Actuaries etc. The strong deviation theorems is one of the central questions for studying in the international Probability theory . In this paper , a class of strong deviation theorems for the sequence of arbitrary integer-valued random variables are obtained by constructing a nonnegative martingale.
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