Convergence Almost Surely
almost surely when , a stronger requirement than convergence in probability.
Definition 5.3 (Convergence Almost Surely)
Let be a sequence of random variables and be a random variable. We say that converges to almost surely (a.s.) or with probability if
We write as almost surely.
Implies convergence in probability
Proposition 5.4
If as almost surely, then .
Related
Stated in
- Definition 5.3 (Convergence Almost Surely)§5.1 Convergence Results
- Proposition 5.4§5.1 Convergence Results