# Math Help - Convergence of a nonnegative submartingale

1. ## Convergence of a nonnegative submartingale

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

2. ## Re: Convergence of a nonnegative submartingale

Hey alphabeta89.

Do sub-martingale always increase (or at minimum, remain unchanged)?

3. ## Re: Convergence of a nonnegative submartingale

Ya, Can I use X_n = n?

4. ## Re: Convergence of a nonnegative submartingale

That seems reasonable, but can you please remind what almost surely refers to?

5. ## Re: Convergence of a nonnegative submartingale

If $X_n$ converge almost surely to $X$, then

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

Right?

6. ## Re: Convergence of a nonnegative submartingale

Well then it looks OK.