(CNN) -- The wife of missing adventurer Steve Fossett has asked a court to declare him dead.



Steve Fossett and wife Peggy in a February 2006 photograph.



Fossett was last seen in early September, flying a single-engine plane on a pleasure flight from a Nevada ranch. A month-long search for the plane was unsuccessful.



"As difficult as it is for me to reach this conclusion, I no longer hold out any hope that Steve has survived," wrote Peggy V. Fossett in court documents filed Monday with the Cook County [Illinois] Circuit Court.



She asked that the will of her husband of 38 years be admitted to probate.



At about 8:45 a.m. on September 3, the millionaire took off on what he said was to be a solo pleasure flight over the Sierra Nevada mountain range.



He had planned to fly over the Nevada desert for two to three hours, and was expecting to return for lunch to the Nevada ranch, from which he departed. He was carrying a single bottle of water and had no parachute, lawyers for Mrs. Fossett said in the court documents.



At 3 p.m., when he had not returned, a search began that ultimately included thousands of volunteers. It continued until October 2.



"No one involved in the search holds out any hope that Fossett is still alive," the petition said.



Rick Rains, a sheriff's supervisor of the San Diego County Sheriff's Department, said Fossett's plane was last spotted at 11 a.m. less than 20 miles from the ranch's airport. "Given the timeline and the sighting of Fossett's plane, I believe he was within 20 to 25 miles of the ranch when he crashed," Rains said.



But, he noted, "the terrain is very difficult to search, with many areas where the crevices, deep ravines and closely grown trees make it impossible to see from the air what is on the ground."



"If Fossett was physically able to find water to survive on in the Nevada desert, he would have been physically capable of signaling searchers, by doing something as simple as crafting a large X of sticks or rocks, or by starting a signal fire," Rains said.



In affidavits supporting his wife's petition, Fossett's doctor described the 63-year-old man as physically and mentally fit.



Robert Keilholtz, a captain in the California Civil Air Patrol who was involved in the search, noted that the difficulty in finding wreckage was underscored by the fact that World War II-era plane wreckage was discovered last spring in the mountain range.



In the search for Fossett, wreckage from eight other crashes was discovered, one of them from the 1960s, the lawyers said.



Fossett made his money in the financial services industry, but is renowned for his daredevil exploits, which include nonstop, round-the-world trips aboard a balloon, a fixed-wing plane and a boat.



At the time of his disappearance, Fossett was working on a project to build a single-man submarine and to build a vehicle capable of breaking land speed records by traveling at up to 800 mph, lawyers for his wife said. E-mail to a friend
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Steve Fossett September, spotted at 11 a.m. less than 20 miles from the ranch's airport. Steve Fossett month-long Nevada ranch. early September, A month-long last seen in early September,
question: Who went missing on a solo flight?, answer: Steve Fossett | question: How long have they been searching?, answer: September, | question: Where was the small plane last sighted?, answer: spotted at 11 a.m. less than 20 miles from the ranch's airport. | question: Who is missing?, answer: Steve Fossett | question: How long was the search?, answer: month-long | question: Where was the single-engine plane last seen?, answer: Nevada ranch. | question: When did Stephen Fossett go missing?, answer: early September, | question: How long has the search been going on?, answer: A month-long | question: How long has Fosset been missing?, answer: last seen in early September,