Betsy Gotbaum called Carol Ann Gotbaum "a wonderful, wonderful person" and a great mother. She said the family was dealing with the situation "the best way we can."

The tech-dominated Nasdaq also gained 1.5 percent for its highest close since February 2001 while the S&P 500 gained 1.3 percent.

CNN and other news organizations did so until the child was found, and De Meo asked media to stop showing the picture.

Stiles was a distant friend of the girl's family, De Meo said.

"You're seeing a continuation of the recent momentum," said Chris Johnson, CEO of Johnson Research Group.

A spokeswoman for the Maricopa County medical examiner said an autopsy would be conducted Monday morning.

Investigators said officers went to check on her five to 10 minutes later. Police policy requires that be done every 15 minutes.

"The mother has cooperated with us," De Meo said. "We believe that the mother was not aware of anything that went on with this young girl. It was very sad for her to find this out."

Finding Gotbaum "unconscious and not breathing," Hill said, officers performed CPR.

"It becomes a psychological phenomenon. Investors know that there are inherent risks in the market, but at the same time, they're rationalizing any bad news."

"Sometime during the time she went into custody, she went into medical distress," he said.

Authorities have identified Chester A. Stiles, 37, as the suspect in the tape. A resident of Pahrump, Nevada, he remains at-large, De Meo said. Pahrump is about 60 miles west of Las Vegas.

"She's what you'd expect a little girl in elementary school to be like," he said. "You would never know something like that happened. Ever."

Gotbaum was the mother of three young children and the daughter-in-law of longtime New York City Public Advocate Betsy Gotbaum.

Someone close to Stiles told investigators Stiles is a "survivalist type" and always carries a weapon, Nye County District Attorney Bob Beckett said.

Todd Allen, a Las Vegas resident, told CNN he once lived with the girl from the video and her mother. He said he recognizes his old apartment from scenes in the video. He said he knows the suspect because Allen's mother dated Stiles and the couple spent time together at Allen's apartment. Watch Allen describe Stiles and the girl »

Allen said nobody realized the child had been abused.

Allen said he never witnessed Stiles physically assault anyone.

"But I have seen him verbally and mentally assault many people," Allen told CNN. "He's good with mind games. He's good at twisting people's realities and manipulating people."

The Dow Jones industrial average added nearly 192 points to end at an all-time high of 14,087.55 points on Monday amid hopes that banks have put the worst of the recent 'credit crunch' behind them and expectations that the Federal Reserve will continue to cut interest rates.

In Asia on Tuesday, Tokyo's Nikkei 225 gained 200 points to close up 1.19 percent at 17,047, its highest finish since August 9. Technology companies Sony (4.2 percent) and Canon (2.6 percent) and automakers Nissan (3 percent) were among the biggest gainers.

"The Nikkei appears to be in a gradual uptrend now," Nobuyuki Nagamorim, a technical analyst at Unimat Yamamaru Securities, told The Associated Press.

"The degree of recovery in trading volume will largely decide how high the market can go," he said.

Hong Kong's Hang Sen was also up 3.89 percent -- gaining more than 1,000 points -- at 28,047.

BAGHDAD, Iraq (CNN) -- British Prime Minister Gordon Brown arrived in Baghdad on Tuesday for meetings with Iraqi government officials, the British Embassy in Baghdad said.

This is Brown's first visit to Iraq since becoming prime minister in June.

The visit comes as unconfirmed reports suggestedBrown was considering a reduction in the number of British troops in the southern Iraqi city of Basra. Reports said as many as 2,000 troops could be home by the spring, according to the British Press Association. The Basra contingent could fall to little over 3,000 in the next six months, the PA reported, citing The Daily Telegraph newspaper.