Wednesday's strong IPO of Fortinet is yet another sign that investors are warming up to early-stage deals -- especially of fast-growing companies.

So does this mean we'll see a public offering of a company like Facebook?

Maybe so. According to Bloomberg News, there has been lots of activity in the private shares of Facebook, which have spiked 42% over the past couple months. The valuation now comes to about $9.5 billion.

Dollar General Store (DG) started as a wholesaler in 1939 and then became a retailer in 1955, when the company setup its first store. Since then, the company has grown rapidly. Now, Dollar General is the largest discount retailer in the U.S. -- that is, in terms of the number of stores (which is currently at 8,577).

A few years ago, Dollar General went private, with the backing of KKR, Citi (C), Goldman Sachs (GS), Wellington Management and the Canada Pension Plan Investment Board. It was at the height of the buyout boom, with a price tag of $7.3 billion. Only $2.8 billion was in equity.

Late Tuesday, The Wall Street Journal reported that Las Vegas Sands (LVS) is preparing to relaunch its stalled construction projects in Macau, China's hot gambling region. Financial woes forced Las Vegas Sands to walk away from the two construction sites a year ago, but newly secured funding means that the casino company can resume work on the projects as soon as January.

Las Vegas Sands disclosed in a regulatory filing on Monday that it secured $1.45 billion in financing from banks, and the firm is looking to lock down an additional $300 million. The gaming issue is also attempting to raise as much as $3.83 billion by launching an initial public offering (IPO) in Hong Kong of its Macau assets, about $500 million of which will be used to fund construction on the stalled sites.

The IPO market has been pretty slow for the past two years due to the effects of a subprime mortgage crisis that turned into a credit crisis that turned into a worldwide financial crisis and recession. Nonetheless, two companies made their debuts Thursday -- one on the NYSE (NYSE: NYX), the other on the NASDAQ -- and they nailed it. Hyatt Hotels (NYSE: H) gave its investors a 12% gain on its first Big Board trading day, and Ancestry.com (NASDAQ: ACOM) switched those digits, jumping 21% in its first day of trading.

Hyatt Hotels overcame two major concerns. The worldwide travel market slump has been tough on hotel companies, and Hyatt has been subject to the same forces as everyone else. Also, investors may have been worried about infighting among the founder's heirs (the Pritzker family), but the double-digit price increase suggests that investors don't foresee Bancroft-style squabbles screwing investors -- or, if you don't like Dow Jones, now a part of News Corp (NASDAQ: NWS), Playboy (NYSE: PLA) makes the same point.

What has Blackstone (NYSE: BX) been doing with all those theme parks it's been buying? Well, the answer is becoming a bit clearer now. The private equity firm is getting ready to take theme park operator Merlin Entertainments public early next year.

Several investment banks have already been called to advise on the transaction, including Citigroup (NYSE: C), Goldman Sachs (NYSE: GS), Deutsche Bank (NYSE: DB), UBS (NYSE: UBS), and Nomura (NYSE: NMR). If all goes as planned, the deal could be good for $3.33 billion.

When you smell an IPO coming, look for Kleiner Perkins Caufield and Byers. The Sand Hill Road institution has a knack for sniffing out high-potential deals and putting its venture capital coffers to work. Mobile phone music discovery service Shazam could have a liquidity event coming, according to the Financial Times, which caught Kleiner Perkins' attention. So, the VC company has decided to take a stake in Shazam.

Up until the credit crisis, private equity firms had it made. They had plenty of leverage to play with and could load up their acquisition targets with it. So, they could realize a fantastic return on equity, mitigate their own risks, and show that they were the studs of the Street.

Then, all that went away. Credit markets dried up, and private equity companies lost their acquisition fuel. The numbers aren't as big as they used to be, but it looks like the private equity market is back in action.

The private equity industry has been through the worst, but now it seems the situation is taking a turn for the better. Stephen Schwarzman, CEO of Blackstone (NYSE: BX) expects deal flow and IPOs to bounce, saying the economy is showing "more than green shoots" of recovery.

Schwarzman, speaking at the Super Return Middle East conference in Dubai, doesn't expect another slip into recession, but the full recovery will take time, for all the same reasons you've been reading on BloggingStocks for a while: tighter lending standards; uncooperative consumers who won't spend beyond their means and so on.

The Blackstone Group (NYSE: BX - option chain) shares are rising today on reports that the buy-out firm is planning to unload a number of its portfolio companies, including TeamHealth, which provides outsourcing services for the health-care industry, and Merlin Entertainments Group, of Europe, which owns Legoland and Sea Life. Up to eight IPOs and five sales to private equity companies are in the works. If you think that the stock won't fall by too much in the coming months, then now could be a good time to look at a bullish hedged trade on BX.

Blackstone opened Monday at $15.50. In morning trading the stock hit a low of $15.50 and a high of $16.18. As of 11:15, BX was trading at $15.79 up 0.94 (6.3%). The chart for BX looks bullish.