Hi, how to I show that a non-negative submartingale need not converge almost surely?

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- Mar 2nd 2013, 07:19 AMalphabeta89Convergence of a nonnegative submartingale
Hi, how to I show that a non-negative submartingale need not converge almost surely?

- Mar 2nd 2013, 09:55 PMchiroRe: Convergence of a nonnegative submartingale
Hey alphabeta89.

Do sub-martingale always increase (or at minimum, remain unchanged)? - Mar 3rd 2013, 12:05 AMalphabeta89Re: Convergence of a nonnegative submartingale
Ya, Can I use X_n = n?

- Mar 3rd 2013, 12:10 AMchiroRe: Convergence of a nonnegative submartingale
That seems reasonable, but can you please remind what almost surely refers to?

- Mar 3rd 2013, 12:41 AMalphabeta89Re: Convergence of a nonnegative submartingale
If $\displaystyle X_n$ converge almost surely to $\displaystyle X$, then

$\displaystyle P(\lim_{n\to\infty}X_n = X) = 1$.

Right?:D - Mar 3rd 2013, 02:23 PMchiroRe: Convergence of a nonnegative submartingale
Well then it looks OK.