Surely ATC would be trying to contact the aircraft once they noticed the descent from FL380? If aviate/navigate/communicate was in play then travelling with no deviation from path, fairly steady ROD/Speed and no radio contact is pretty strange. I have not seen/heard any information about ATC trying to make contact. Very sad news and hopefully the investigating parties will release details from the CVR/FDR quickly to stop the more extreme speculation.
Reports that ATC had tried to make contact numerous times, and with no response had initiated the scrambling of a military jet to investigate