- 24. Let
be a probability space and let 
be a Poisson process with intensity 
and 
be a standard Wiener process relative to the same filtration 
, 
. By considering the process
where
, use Itō's formula to find an SDE for 
.By setting
show that solution to the SDE can be expressed as
Solve the differential equation to find and deduce that .
Solution
By expanding using Taylor's theorem and taking ...
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