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0 $begingroup$ Let be $B$ standard Brownian motion and let $S leq T$ two stopping times with $E(T) < infty $ and $E(S) < infty$ . Prove that hold $$ E[(B_T - B_S)^2] = E[B_T^2 - B_S^2] = E(T-S).$$ Please help me solve this. stochastic-processes stochastic-calculus brownian-motion stopping-times share | cite | improve this question asked Jan 11 at 20:34 user631885 $endgroup$ add a comment  |