On Mar 28, 10:23 am, hru...@[EMAIL PROTECTED]
(Herman Rubin) wrote:
> In article
<95b06732-3d1a-4eb9-bd81-2a8c7e7bd...@[EMAIL PROTECTED]
>,
> Luna Moon <lunamoonm...@[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.
>
Hi Herman,
No the model is a GBM with no drift, so lambda_t won't be negative.
> -----------------------
>
> >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!
>
Any pointers about books, etc. ?
Thanks
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