June 29th, 2008, 2:27 pm
No, but you can do this. There is a class of pure-jump Levy processes called alpha-stable processes,where alpha is a parameter in (0,2). As alpha -> 2, you get a Wiener process. The sample path for,say, alpha = 1.9 consists of nothing but jumps but neverthelessl looks a lot like Brownian motion. Unlike a Poisson process, thejump intensity is infinite and the jump sizes are variable. See Cont & Tankov's book for more.Hope it helps,