i guess you can try finding an emulator for PS2, or just buy the games, PS2 games are pretty cheap nowadays, check ebay for second hand ones as well
The answer is yes, however I have stress, you will need a VERY heafty computer! I've tried and I got like 10-15 FPS. You will need AT LEAST the following: Dual Core (3.0 Ghz or better) Quad Core recommended! nVidia Geforce 8800 GTX or better (512 MB) A good DVD R Drive with like 32x or so speeds. Also, you need to have a PS2 in order to use it because you have to "dump your Bios" from your PS2. Although if you're sneaky enough I'm sure someone has it on the internet.
If you want to play PS2 games on PC, you need to have high spec PC to play the games using emulator. Just get a PS2, they're pretty damn cheap nowadays.
my friend there is no such things as psp2 there is only ps2 and psp the other version of psp is slim than the previous 1