In my experience in this firstly you have to determin the difference between a simple dream and a premonition ,but that is when you have them so it is difficult
But anyway yes i do believe in them as i have had a few of these myself ,the strange thing i found is that even thoe it scares hell out of you when you wake up after having a premonition and you dont worry about it after awhile ,and then BANG it hits you because something happens and you know how and sometimes why ,that is when you start to look further into this