My MacBook, in which i had installed my Logic Studio was stolen. How can i re-install Logic Studio to my new MacBook?

If you log into the App Store, you can click on the Purchases icon at the top of your screen. There you can download any previously purchases applications.

If you've backed-up your stolen mac using Time Machine, then restoring from that backup onto your new computer should also bring all your old apps back.

If the copy you purchased was legal and legitimate, then you should be able to contact Apple support for help.

If this reseller was unscrupulous, and sold you an illegtimate copy, then you might have to repurchase it from Apple.