My question is about limiting r.v.
Suppose, we have a sequence of r.v.s. $\{X_n\}$. And we know that $\liminf X_n=-\infty$ and $\limsup X_n =\infty$ almost surely. What can we say about $\lim X_n$. Does it exist?
Thank's!
2026-04-01 07:21:07.1775028067
Limiting random variable
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No, and this really has nothing to do with randomness. In order for $\lim X_n = L$ to exist, you need $\liminf X_n = \limsup X_n = L$.