Definition: Yo,Y1,...is a martingale with respect to Xo,X1,... if,for all i≥0， .Yi is a function of Xo,X1,...,Xi; .E[Yi+1 Xo,...,Xi]Yi. Betting on a fair game; Xi:win/loss of the i-th bet; Yi wealth after the i-th bet--Martingale(fair game)Definition: Y0,Y1,... is a martingale with respect to X0,X1,... if, for all i ￾ 0, • Yi is a function of X0,X1,...,Xi ; • E[Yi+1 | X0,...,Xi] = Yi . • Betting on a fair game; • : win/loss of the i-th bet; • : wealth after the i-th bet -- Martingale (fair game) Xi Yi