NEW YORK, DEC. 7 -- Blue-chip stocks rose in light trading today but the rest of the market was mixed, and analysts cautioned against interpreting the session's narrow rally too optimistically. The dollar firmed against most major currencies in quiet trading.

The Dow Jones average of 30 industrials jumped 45.43 points to close at 1812.17, a 2.57 percent rise and the indicator's 14th largest point gain.

While the Dow average's climb appeared healthy, volume remained relatively low and the broader market showed only a slight price increase, indicating that "this is not a strong market," said Hildegarde Zagorski, a market strategist with Prudential-Bache Securities Inc.

Gainers outpaced losers by a 9-to-7 ratio on the New York Stock Exchange, with 902 stocks up, 703 down and 387 unchanged.

As measured by Wilshire Associates 5,000 Equity Index, stocks rose $35.25 billion in value.

Big Board volume totaled 146.66 million shares, down from 184.80 million in the previous session.

Analysts said the market gained on the strength of a firmer dollar in foreign exchange. They said foreign investors, who were encouraged by speculation that the Reagan administration's policy has shifted in favor of supporting the dollar, did most of the buying.

"There was an influx of foreign buying, particularly the Japanese," who stepped in early in the day in search of blue-chip issues, said Michael Metz, a market strategist with Oppenheimer & Co.

Domestic investors remained bearish, however.

"The sellers decided to step away" and see where the market would go, said Metz, noting that there was not a great resurgence in demand.

While some blue-chip issues enjoyed sustained price gains, "the majority {of the stocks} the public owns -- the secondaries -- were still under some patch pressure," said Jack Solomon, an analyst with Bear Stearns & Co.

Analysts were reluctant to predict whether the market had bottomed and that the day's rise could portend larger gains ahead. "It is a very suspect rally," Metz said.

"People just don't trust {the market}. They're skeptical," Solomon said. But that environment of pervading pessimism "could permit the market to rally when everyone is asleep at the wheel," he said.

Gold prices edged lower in domestic activity. Republic National Bank of New York quoted gold bullion in late afternoon at $481 a troy ounce, down from $482.50 late Friday.

Foreign-exchange analysts said year-end trading was giving the dollar some support as traders closed out speculative positions.

"Call it short-covering or clearing the books. ... People are taking profits and shutting down for the year," said Karen Gibbs, an analyst for Dean Witter Reynolds Inc. in Chicago.

In late New York trading, the dollar brought 132.98 Japanese yen, up from 132.30 late Friday and 1.6790 West German marks, up from 1.6682. The pound fetched $1.7856, down from $1.7935.

Among today's gaining stocks, Teledyne rose 4 1/2 to 274, Dow Chemical gained 4 1/4 to 76 1/2, Digital Equipment increased 4 to 117 3/4 and Merck was up 4 3/8 to 157 7/8.

Other advancers included Telex, which rose 9 3/4 to 51 1/2 after the company announced it had received an acquisition proposal from Memorex International NV.

Losing issues included Honeywell, down 1 to 51 3/4, and Allied Signal, which fell 3/4 to 26 1/8.

Banking issues came under pressure as Argentina said it might pose a moratorium on debt payments to foreign institutions. The Federal Deposit Insurance Corp. also said today that the nation's banks may end the year with the lowest overall earnings since 1934.

Manufacturers Hanover fell 1 3/8 to 24 7/8, Chase Manhattan declined 1 to 21 7/8, Citicorp dropped 3/4 to 16 5/8 and Chemical fell 1/2 to 23 3/4.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 170.98 million shares.