A Strong Limit Theorem for Fair Game and the Approach of Conditional Moment Generating Function
Yanling Li · Journal of Hebei University of Technology · 2006
A strong limit theorem on gambling strategy for Bernoulli sequences is extended to the sequences of arbitrary dependent random variables which take numberable values by using the conditional moment generating function. Further- more, by allowing the selection function to take values in an interval, the conception of random selection is generalized. In the proof, an approach of applying the differention of measure on a net to the investigation of the strong limit theorem for gambling system is proposed.