Wiktionary
adv. (context idiomatic English) alone; by oneself; without the companionship or assistance of others.
WordNet
adj. responsible for yourself; "now out of college and on their own" [syn: on one's own(p), on his own(p), on her own(p), on your own(p), on their own(p)]
Usage examples of "on one's own".
It was frightening enough to face it on one's own, but with Jenny - 'Why don't you drop the idea of coming with us?
At any rate, it would be a good idea to practice one's somewhat rusty skulking skills again to determine who the person was and assure oneself of the Princess Anastasia's safety before one set off on one's own adventure.
Striking out on one's own without a carrier to dreamride was tricky.
He had already decided that it was better to be an independent operator, on one's own or, at the most, hooked up with a partner.
But there was no substitute for swimming that sea on one's own, unfettered and unencumbered, at one with all of creation.
To a place like this one had to come walking firm and heavy on one's own two feet, just in case when they did the analyses they thought to check for what was usually there, but according to people who should know the end-products should be flushed out by a thirty-six hour abstinence, which was freefalling.