Suppose that a gambler places bets at discrete times t = 1,2,..., and that his fortune after the n’th bet is the random variable Xn. (Thus X 0 is the initial stake, and in general the Xn’s can take positive or negative real values.) How can we express the idea that the sequence of bets is “fair”?
KeywordsConvergence Theorem Martingale Theory Fair Game Integrable Random Variable Hand Limit
Unable to display preview. Download preview PDF.