Thanks for your answers! I didn't know that about DMA, so I think I need further reading material about how a DMA transfer is initiated and controlled by the host CPU (more detailled than [1]). Any suggestions?
Is there really no way to access the systems RAM without initiation by the host's CPU?
@lastchancename: We do not want to access the Arduino's RAM - we want to access the hosts RAM. Without any additional software on the host, if possible. As I said, it's for a security research project, so installing custom software on the host before launching the attack is ridiculous 
Sebastian