The homebrew community has beaten Sony to the punch, releasing the first PlayStation (1) emulator for PSP, called PSX-P. But, as this is simply the first public beta version, the emulator suffers from speed issues, among other defects. Riiiiidge Racer
is reported to clock in at a paltry 10 fps.
PSX-P is compatible with PSP firmware v1.00–2.71 (an eLoader is necessary beyond firmware v1.50).