Is it possible that N_t and W_t be dependent?

bquant · April 14th, 2008, 2:24 pm

I have done an excercise to prove that the Poisson process N_t and Brownian motion W_tare independent given that they are adapted to the same filtration F_t.My question: is it possible that N_t and W_t are actually dependent under some condition?

Alan · April 14th, 2008, 3:37 pm

I have never seen that for the 'pure' Poisson process, but small generalizations can be dependent.For example, with a stochastic intensity you could have lambda_t = lambda(W_t), or a compound Poisson,where the jump size (distribution) depends on W_t. regards,

bquant · April 14th, 2008, 3:59 pm

thank Alan.