Stocks in the United States tumbled today, following steep slides on Asian and European markets.

But the selling here was relatively calm, compared with the panicked unloading of equities that marked trading on overseas market earlier in the day.

Indeed, stocks cut their losses late in the day. The Dow Jones industrial average, which fell more than 500 points in early trading, ended the day down 312.30 points, or 3.6 percent. The Standard & Poor's 500-stock index fell 31.35 points, or 3.5 percent. For the week, the S&P was down 6.8 percent, the Dow was down 5.4 percent, while the technology-heavy Nasdaq composite index lost 9.3 percent.

Writing earlier in the day, James Surowiecki noted on his blog that “it is a sign of how crazy this market is that a 4 percent downward move seems almost normal.”

Still, more than $10 trillion in the value of stocks has been wiped out this month, Bloomberg News estimates. (Talk about a Red October.)  That sell-off has been prompted by one big company after another reporting weak earnings or expecting a slowdown ahead. Much of the world is sliding into a recession.

Yet at first, today looked like it would be turning into something much worse. What changed, starting in Asian trading, was a brake-squealing U-turn in the mood of investors around the world. Investors in the United States assumed the crash position for what Wall Street professionals call a "capitulation."  But the white flag never flew.  As stocks plummeted, buyers dove in, looking for bargains, and some lost ground was recovered.

The stock market is a tragi-comedy that has not yet played its final scene. There will be more wrenching sell-offs followed by strained recoveries. Offstage, additional financial institutions will quake and the government will be forced to attempt rescues.

Signs of the vast global deleveraging as hedge funds and others dump assets were evident on other markets. Many currencies tumbled in value against the Japanese yen, as carry-trades were unwound.  Oil prices continued to fall even after Opec announced that it was cutting its production limits.  And doubts  reemerged about the credit markets, which after a long freeze, had been showing signs of thawing. But today, the dollar overnight Libor rose 7 basis points, to 1.28 percent.  Credit-default swaps  on U.S. investment-grade debt widened.  Prices of Treasury securities, a traditional safe haven in times of market turmoil, climbed. The yield on the 30-year Treasury bond, which moves in the opposite direction from the price, fell to the lowest it has been since 1977. 

The global wave of selling in stocks today began in Tokyo, where Japanese stocks fell nearly 10 percent to their lowest levels in more than five years. A profit warning by Sony on Thursday weighed on that market. Hong Kong fell 8.3 percent, while Seoul tumbled 10.6 percent.

European markets were sharply lower. London stocks fell 9 percent after data showed that the British economy contracted in the third quarter.

Frankfurt was also down 9 percent; Paris slid 8 percent. Shares of banks and automakers were among the weakest.