U.S. military authorities in Germany say Airman 1st Class Spencer Stone is doing well at an American military hospital where he is being treated for injuries suffered as he and others helped subdue a heavily armed gunman on an Amsterdam-to-Paris train last Friday.

Landstuhl Regional Medical Center spokesman Chuck Roberts said Tuesday that Stone arrived at the facility in southern Germany the day before and seemed in good spirits, smiling and shaking hands with leaders of the U.S. military hospital.

He says Stone is being treated for a laceration to his thumb, for which a full recovery is expected with ongoing therapy, as well as a "non-critical" eye injury and more minor wounds.

It's not yet clear when Stone will be transferred back to the U.S.