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This is a question from Durrett's book Probability Theory and Examples (Third edition, page 237.)

Give an example of a martingale $X_n$ with $\sup_n|X_n|<\infty$ and $P(X_n=a\;\;i.o)=1$ for $a=-1,0,1. $

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No. See the FAQ. – Steve Huntsman Jul 11 2011 at 19:02
Sorry Remo. This site is not appropriate for your kind of question: this site is exclusively reserved for research level math. MathStackexchange is another site for somewhat lower level questions. – André Henriques Jul 11 2011 at 21:35

closed as too localized by Steve Huntsman, Yemon Choi, André Henriques, Andreas Blass, George Lowther Jul 11 2011 at 22:49

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