The Romans conquered the Greeks politically, but culturally the influence went mainly in the other direction, and in fact the Meditations (per my comment at https://news.ycombinator.com/item?id=8580261) were written in Greek.
Graecia capta ferum victorem cepit et artes intulit agresti Latio. - Ep. II.i.156
"Greece, once conquered, herself conquered the artless victor, and planted the banner of civilization in the farmlands of Rome."
I have translated freely and taken considerable license.
By Aurelius' time, familiarity with Greek for the ruling classes was a given; as a matter of preference, it is a more supple language and probably more comfortable to use for putting abstract reasoning to words.
Marcus Aurelius wrote the Meditations in Greek, which was the language of philosophy in the ancient Mediterranean. It was not uncommon at the time for wealthy Romans to have Greek slave-teachers ("pedagoges") instruct their children in the Greek language, as well as other subjects.
Edit: Incidentally, a simple Google would've shown it was written in Greek: http://en.wikipedia.org/wiki/Meditations
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