Hi all,
I am wondering if the following process can exist in a suitable
probability space P?
It is a Poisson type process, but its intensity lambda_t is specified
by
d(lambda_t) = sigma*lambda_t*dBt,
where Bt is a standard Brownian Motion.
Basically, I want to see if it is okay to specify the intensity in
terms of the Brownian Motion.
-----------------------
If such jump process does exist, I want to apply a change of measure
to it and obtain, under the new measure Q,
a standard Poisson process with intensity 1.
The Radon Nikodim derivative formula for such a change of measure is
available in many books.
However, I am not sure if the standard Brownian Motion Bt is still a
standard Brownian Motion under the new measure Q?
Moreover, if the answer is YES, then the standard Brownian Motion and
the standard Poisson process are independent under Q?
Thanks!
|
