Sony's has posted a PS Vita FAQ to its Japanese PlayStation site, revealing that the company may plan on offering discounted digital downloads for the UMD games PSP gamers have amassed over the years.
The FAQ includes the question "Can PS Vita play PSP Games?" The answer is yes, but only via digital downloads. Sony does go on to say that those who already own the UMD of a game may be offered a discounted digital version for PS Vita.
It is unclear if Sony is considering this program outside of Japan. Remember that Sony contemplated implementing a similar program for PSP Go buyers whose library of UMDs would be useless on the all-digital console. That program never actually panned out, so don't go selling your PSP just yet.