A Class Of Strong Deviation Theorems For The Sequence Of Nonnegative Integer-Valued Random Variables

Gambling problem has always been an old problem in the development of Probability. V.Mises firstly found that under the assumption of fair gambling there were no succesful policies which could change the gambler's fourtune. In recent ten years, Professor Liu Wen and his counters have done a lot of works about the strong limit theories of gambling system. This paper is trying to make some improvements and do some further study on the basis of previous works. For example, I have extended the conception of random selection functions and introduced the conception of profitlio. The purpose of this paper is to investigate this problem by means of submartingale.