The former Playmate confirms that she's expecting in a video message on her Web site

Anna Nicole Smith is finally putting to rest rumors that she’s pregnant – by confirming that she is with child, as she reveals in a video clip posted on her Web site.

Floating on an inflatable raft in a swimming pool and with a dog barking in the background as she looks directly into the camera, the former Playmate and reality star says: “Well, let me stop all the rumors. Yes. I am pregnant. I’m happy, I’m very, very happy about it. Things are goin’ really, really good, and I’ll be checking in and out periodically on the Web, and I’ll let you see me as I’m growing.”

There are no further details in the posting, such as how far along she is or who fathered the baby.

Early last month, playing along with the rumors that were rising, Smith’s attorney, Howard K. Stern, said in a written statement: “If Anna Nicole is pregnant she obviously doesn’t want anybody to know yet. If she is not pregnant she’s not denying the rumor because she thinks it’s funny how much of a stir it’s causing. She’ll leave it up to you to guess which one it is.”

The rumors had followed published reports that the 38-year-old former pinup and weight-loss pitchwoman was pregnant by an unidentified man.

Smith already has a 20-year-old son, Daniel, from a previous relationship.

Meanwhile, the same week as Stern’s statement, Smith won a U.S. Supreme Court ruling that gives her another chance to collect millions of dollars from the embattled estate of her late Texas oil tycoon husband J. Howard Marshall.

Smith married Marshall in 1994 when she was a 26-year-old topless dancer and he was an 89-year-old Texas oil tycoon. Marshall died the following year.

His son, Pierce Marshall, claims his father’s various wills and trusts make him the sole heir of a fortune estimated to be as high as $1.6 billion – which triggered the family feud that has been played out in courtrooms in both California and Texas and then, finally, in the Supreme Court.