The Greco-Roman world kept its own end-times doctrine, and it came not from oracles but from physicists — for that is what the early Stoics understood themselves to be.
The doctrine
Zeno, Cleanthes and Chrysippus taught that the cosmos is a living thing pervaded by divine fire, and that at vast intervals it resolves entirely back into that fire — ekpyrosis, the conflagration — before unfolding again. And not merely again: identically. In the reconstituted world, the fragments report, there will be another Socrates, another Athens, everything down to the smallest detail, because the same divine reason unfolding from the same seed-state can produce nothing else. History does not merely rhyme; it repeats to the letter, without limit.
Marcus Aurelius, thinking it through
Four centuries later the doctrine was contested even among Stoics, and the Meditations show a working mind holding it lightly. Marcus returns constantly to the disjunction "providence or atoms," and to the cosmos's rhythm of change — the universe is change; life is opinion, and again, that the nature of the whole ever makes new things in succession out of what has been. Whether all things recur exactly or merely dissolve and recombine, his practical conclusion is identical: nothing is lost that was ever truly yours, and the present moment is the only possession. We keep the whole text in the Study Hall — read the Meditations verse by verse.
What the Stoics did with their apocalypse
Here is the striking thing: a school that believed the world would burn built the calmest ethics in antiquity on that belief. The conflagration was not terror but perspective — proof that the whole is ordered, that endings belong to the pattern, and that the task meanwhile is unchanged: justice, self-command, and assent to what is. Compare the Bhagavata's move — darkest description, easiest remedy (the Kali Yuga passage) — and the Völuspá's green earth after the fire (Ragnarok). The traditions keep agreeing: cosmology is for conduct.
Related
Impermanence across the traditions · On death · The Meditations