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April 2nd, 2009, 12:00 PM  #1 
Newbie Joined: Apr 2009 Posts: 1 Thanks: 0  martingale crossing probability
Helle everybody, I was reading through a proof within a paper and found one fact I could not explain myself: We have a stochastic process (X_t); t>=0 and X_t is a martingale, It is said in the paper that "it is a wellknown fact that the probability that a martingale with initial position y (X_0 = y) , defined on a state space (0,l), will ever hit zero, is 1 y/l" > P(inf{X_s: 0<=s<=\infinity} = 0) = 1 y/l. Unfortunately I could not find any similar facts in the literature. Maybe somebody can give me some hints. Thanks forward! 
April 22nd, 2009, 07:31 AM  #2 
Newbie Joined: Apr 2009 Posts: 1 Thanks: 0  Re: martingale crossing probability
Hint : Express with respect to condition and its complementary event and use optional sampling theorem


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