4ns
@fourenes.bsky.social
Stats @ Duke. Stochastic process enthusiast
Want to share my favorite example ever. Perfectly shows that convergence in p doesn't imply convergence a.s. The idea is that, though clearly we are converging to 0 in probability, we can always find omega and m >= n (for all n) such that X_m(omega) = 1 (*I think LHS of last line needs ->0 in {})
November 19, 2024 at 3:57 PM
Want to share my favorite example ever. Perfectly shows that convergence in p doesn't imply convergence a.s. The idea is that, though clearly we are converging to 0 in probability, we can always find omega and m >= n (for all n) such that X_m(omega) = 1 (*I think LHS of last line needs ->0 in {})