It's a Girl for Jason Schwartzman

Marlowe Rivers arrived Dec. 4 and is the first child for the actor and wife Brady Cunningham

Photo: Alex J. Berliner/BEImages

Jason Schwartzman is too busy to be Bored to Death – he has a new baby at home.

The actor and wife Brady Cunningham welcomed a daughter, Marlowe Rivers Schwartzman, on Saturday, Dec. 4 in Los Angeles, his rep confirms to PEOPLE exclusively.

“I’m lucky I found a woman that I love and that’s amazing,” Schwartzman, 30, who stars in the HBO hit Bored to Death, said last fall.

“I’m having a family and I feel very happy. I try to be a good father-to-be. I try to treat my wife well [so she can] enjoy these months.

Schwartzman and Cunningham, a fashion designer, wed in July 2009.

• Reporting by OLIVER JONES