# Stopping times – Limit of the stochastic process.

Consider any stochastic process. $${X (t) } ^ {+ infty} _ {t = 1}$$ with $$t = 1,2, …$$ that diverges to $$+ infty$$ almost sure
For any $$L in mathbb {R}$$, leave $$p (L)$$ denotes the probability that $$X (t) for some $$t$$.
Try out $$lim_ {L to – infty} p (L) = 0$$.

I have been trying to prove this for a while for my financial research and I have not managed to do so. Could someone give me an idea? Thank you.