Peggy Fossett asked the court to set in train the distribution of her husband's assets, which run to hundreds of millions of dollars.

"As anyone can imagine, this is a difficult day for our family," she said in a statement.

"We will continue to grieve and heal, but after nearly three months we feel now that we must accept that Steve did not survive."

The search for Fossett was called off in early October, after an intense operation involving rescue planes, ground vehicles and satellite technology succeeded in finding other missing cases from up to 40 years ago but which ultimately failed to locate him.

Fossett went missing on September 3 after he took off on a short pleasure flight from the Nevada retreat of the Hilton family.

He carried only one bottle of water with him, had left no flight plan and was not wearing a watch which acted as a GPS alert that could have notified rescuers to his location.

"Even if Fossett had survived a crash uninjured, which statistics show to be very unlikely, without water Fossett could not live more than a few days," his friend Mark Marshall told the court.

Court papers said that Fossett's wealth was "vast, surpassing eight figures in liquid assets, various entities and real estate".

Fossett made his fortune on the commodity markets before turning to his real passion for daredevil adventures including ballooning and sailing around the world and the 1,150-mile Iditarod sled race across the Alaskan wilderness.