Jesse Kleberg is the son of Max Kleberg from another marriage besides his last one with Peyton. Jesse liked living off Max's money, but he also secretly had a gambling problem, so he nearly stole Peyton's jewelry. When the couple found out, Jesse was cut off from them, assuming he had drug problems.
When Max was killed and Peyton was raped, Jesse was suspected when the jewelry was missing from the burglary. Jesse admitted his gambling problem, and his mother Marilyn Dunlap provided his legal defense. Marilyn revealed his womanizing, which led to the real motive for the attack and acquitted Jesse. (SVU: "Tangled")