A HAWKER800 FLT CREW IN CRUISE ON A TRANSOCEANIC FLT EXPERIENCED DECREASING AIRSPEED. THEY USED EMER AUTHORITY TO DSND AFTER CTR DENIED THEM A LOWER ALT.

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ON A FLIGHT FROM ZZZ TO ZZZZ; AS PLT IN COMMAND; I WAS REQUIRED TO TAKE EMER ACTION TO DSND FROM FL410 TO FL390 AFTER BOTH AIRSPEED INDICATORS SHOWED AN UNEXPLAINED DRAMATIC DECREASE IN INDICATED AIRSPEED. I ADVISED ATC IMMEDIATELY THAT I HAD A PROBLEM AND NEEDED AN IMMEDIATE DSCNT. I WAS TOLD THAT THE CTLR WOULD TRY TO WORK OUT THE PROBLEM WITH CENTER; BUT THAT I WAS NOT CLRED TO DSND. WHEN THE INDICATED AIRSPEED APCHED THE MINIMUM CONTROL SPEED OF THE ACFT; I AGAIN CALLED AND ADVISED ATC THAT I WAS APCHING MINIMUM CONTROL SPEED AND ABSOLUTELY REQUIRED AN IMMEDIATE DSCNT AS I COULD NO LONGER MAINTAIN FL410. ATC ADVISED ME THAT ALL AIRSPACE WAS BUSY AND THAT WE WERE ASSIGNED FL410. AT THAT POINT; I ADVISED ATC THAT; AS PLT IN COMMAND; I COULD NO LONGER MAINTAIN FL410 AND THAT I WAS BEGINNING AN EMER DSCNT OUT OF FL410. THIS WAS IN ACCORDANCE WITH ALL OF MY TRAINING AND INSTRUCTION. DURING THE DSCNT MY CO-PILOT AND I BOTH MONITORED TCAS; AND NOTED NO TFC ADVISORIES OR CONFLICTS WHATSOEVER. ONCE IN LEVEL; CONTROLLED FLT; I CONTACTED CENTER AND REQUESTED INSTRUCTIONS. I WAS ADVISED TO CONTACT FAA WITH REGARD TO A 'POSSIBLE PILOT DEVIATION;' AND GIVEN THE NUMBER TO CALL ONCE ON THE GROUND. I WAS CONCERNED THAT THE DECREASE IN AIRSPEED WAS A SYMPTOM OF SOME PROBLEM WITH THE ACFT; SO I ELECTED TO REQUEST A CLRNC TO OUR MAINT BASE AT ZZZ1. THE CLRNC WAS GRANTED. ON APCH TO ZZZ1 OUT OF 16000 FT; WE GOT A MASTER CAUTION WARNING AND A 'PITOT HEAT FAIL' INDICATION. WE LANDED IMMEDIATELY. THE MAINT FACILITY FOUND THAT THE HEATING ELEMENT IN THE RIGHT PITOT TUBE HAD FAILED. THIS WAS THE CAUSE OF THE ERRONEOUS AIRSPEED INDICATION AT ALTITUDE.IT ONLY TOOK A 2000 FT DSCNT FOR OUR AIRSPEED INDICATORS TO BEGIN READING NORMALLY. A CONTRIBUTING FACTOR WAS THAT THE WX OUT OF OUR DEP POINT AND DURING OUR CLIMB TO FL410 WAS HORRIBLE; WITH COLD RAIN. I CONTACTED THE FAA AS REQUESTED AND EXPLAINED THE SITUATION. I ALSO PROVIDED THE INSPECTOR WITH THE SUBSEQUENT MAINT RPT INDICATING THAT I HAD; INDEED; HAD A FAILURE OF THE PITOT-STATIC SYSTEM WHICH HAD CAUSED ERRONEOUS AIRSPEED INDICATIONS FROM WHICH IT APPEARED THAT WE WERE RAPIDLY LOSING AIRSPEED TO A POINT AT WHICH; HAD THE READINGS ON BOTH ASI'S BEEN ACCURATE; WE WOULD HAVE LOST CONTROL OF THE ACFT HAD WE ATTEMPTED TO MAINTAIN LEVEL FLT AT FL410. I FEEL THAT MY ACTIONS WERE THE MOST APPROPRIATE UNDER THE CIRCUMSTANCE. ALTHOUGH IT MIGHT HAVE BEEN POSSIBLE TO DETERMINE THAT THE AIRSPEED INDICATORS WERE INACCURATE; AND THAT THE ACFT WAS ACTUALLY PERFORMING ADEQUATELY TO REMAIN AT ALTITUDE SAFELY; THE CONSERVATIVE AND SAFE ACTION WAS TO ELECT TO TREAT THE INDICATION AS ACCURATE AND GAIN A SAFE ALTITUDE. I WAS SURPRISED THAT; EVEN THOUGH THE FAILURE WAS CONFINED TO THE RIGHT PITOT TUBE; THE ENTIRE DUAL SYSTEM FAILED AND BOTH ASI'S SHOWED ERRONEOUS READINGS. I BELIEVE THAT THE REDUNDANCY OF THIS SYSTEM ON THE HAWKER 800; AND ON OTHER SIMILAR ACFT; SHOULD BE COMPLETELY INDEPENDENT SUCH THAT THE FAILURE OF ONE PORTION OF THE SYSTEM WILL NOT CAUSE ALL INDICATORS TO SHOW THE SAME ERRONEOUS READING. HAD ONLY ONE ASI SHOWN AN ERRONEOUS READING; MY CO-PILOT AND I COULD HAVE RESOLVED THE CONFLICT IN INDICATIONS WITHOUT FEELING THAT WE WERE IN AN EMER SITUATION. WITH REGARD TO OUR DSCNT; I BELIEVE THAT ATC SHOULD HAVE CLRED US FOR THE DSCNT AND ADVISED US TO MONITOR OUR TCAS TO AVOID TFC CONFLICTS. WE HAVE THE TECHNOLOGY TO DO THIS SAFELY (AND; IN FACT; WE DID SO). WE SHOULD HAVE BEEN ALLOWED TO USE IT AND TO INITIATE OUR DSCNT EARLIER TO ALLEVIATE THE PRESSURE ON ALL CONCERNED AT THE TIME.