U.S. stocks steady, Brent crude hits 4-year low NEW YORK (Reuters) - U.S. stock prices were little changed on Tuesday, hovering near Monday's record closes, while the dollar rose as investors weighed the prospect of further stimulus to aid the recovery of the global economy. Oil prices fell further on the stronger dollar and robust output from U.S. shale fields, with Brent crude dropping to a four-year low below $82 a barrel. "We have equity demand driven by the perception of improving economics and companies' earnings prospects," said Andre Bakhos, managing director at Janlyn Capital LLC in Bernardsville, New Jersey. In mid-morning trading, the Dow Jones industrial average .DJI was up 10.63 points, or 0.06 percent, at 17,624.37. The Standard & Poor's 500 Index .SPX was up 1.70 points, or 0.08 percent, at 2,039.96. The Nasdaq Composite Index .IXIC was up 3.04 points, or 0.07 percent, at 4,654.66. European shares were boosted by positive results from companies including Germany's Henkel (HNKG_p.DE) and Hochtief (HOTG.DE). The pan-European FTSEurofirst 300 index .FTEU3 rose as much as 0.5 percent before retreating to a 0.3 percent gain. Earlier, a 2.1 percent rise propelled Tokyo's Nikkei .N225 to its highest close since October 2007 on speculation that Prime Minister Shinzo Abe might postpone a sales tax hike planned for next October and call a snap election. The MSCI world equity index .MIWD00000PUS, which tracks shares in 45 nations, was little changed at 420.18. The rally in Japanese stocks helped push the yen lower versus the dollar. The greenback hit a seven-year high against the Japanese currency, hitting a seven-year high of 116.11 yen JPY= in European trading on the EBS trading system. The euro EUR=EBS was little changed at $1.2420, not far from a two-year low of $1.2358 hit on Friday. In the bond market, yields on lower-rated Spanish and Italian government bonds fell after European Central Bank Executive Board member Yves Mersch said on Monday that the "critical" state of the euro zone economy made ECB purchases of government debt possible. The U.S. bond market was closed for the Veterans Day holiday. In the energy market, Brent crude futures LCOc1 in London fell 79 cents, or 0.96 percent at $81.55 a barrel after hitting a four-year low of $81.23. It has lost nearly 30 percent since June, partly due to rising production, especially in the United States. U.S. crude CLc1 was last down 20 cents, or 0.26 percent, at $77.20. Spot gold XAU= rose $4.77 or 0.41 percent, to $1,154.90 an ounce, rebounding from a 2 percent drop on Monday, as bargain hunters emerged. Additional reporting by Chuck Mikolajczak in New York; Nigel Stephenson and Francesco Canepa in London; Lisa Twaronite and Shinichi Saoshiro in Tokyo, Ian Chua in Sydney; Editing by Dominic Evans and Dan Grebler