Hi, how to I show that a non-negative submartingale need not converge almost surely?
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Hey alphabeta89. Do sub-martingale always increase (or at minimum, remain unchanged)?
Ya, Can I use X_n = n?
That seems reasonable, but can you please remind what almost surely refers to?
If $\displaystyle X_n$ converge almost surely to $\displaystyle X$, then $\displaystyle P(\lim_{n\to\infty}X_n = X) = 1$. Right?
Well then it looks OK.
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