In article
<95b06732-3d1a-4eb9-bd81-2a8c7e7bd73f@[EMAIL PROTECTED]
>,
Luna Moon <lunamoonmoon@[EMAIL PROTECTED]
> wrote:
>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.
You can do this IN PRINCIPLE, but you would have to specify
what happens if you get something negative. The model above
does not exclude that.
-----------------------
>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!
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@[EMAIL PROTECTED]
Phone: (765)494-6054 FAX: (765)494-0558
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