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April 2nd, 2009, 12:00 PM   #1
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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 well-known 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!
Brainyboy is offline  
April 22nd, 2009, 07:31 AM   #2
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Re: martingale crossing probability

Hint : Express with respect to condition and its complementary event and use optional sampling theorem
TheBridge is offline  

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