Multiple and intermittent primary flight display and autopilot problems occurred on a B737 during cruise. Crew elected to continue to destination.

Narrative

Our flight was about 200 miles northeast of Las Vegas and we were climbing from FL380 to FL400 after burning enough fuel to climb higher. This was routine. A few minutes after reaching FL400; the power levers retarded to idle; the over speed clacker was heard and the Primary Flight Display on the Captain's side was showing completely inaccurate airspeed; altitude and vertical speed information. The 'A' autopilot disengaged as well. The First Officer's Primary Flight Display was unaffected so I transferred control of the aircraft to him by making his flight director the master. We ran numerous QRH checklists but the problem still persisted. Since the First Officer's side was not affected; I elected to continue on to our destination. I then started a descent to FL360 to give us more buffet margin in case the false airspeed indications continued. As soon as we left FL400; all problems with my PFD stopped and everything was normal for the rest of the flight. I elected to let the First Officer land the aircraft just in case my PFD malfunctioned again. I also chose to continue based of the lower terrain since this flight was at night. Maintenance met us and performed numerous tests. The cause was not immediately identified but the FMC showed 48 events of a malfunctioning ADIRU-1.