e use technique of the previous section to calculate the operator
( Backward Kolmogorov operator)
for the
process
where the Poisson process
has the intensity
 .
Similarly to the previous
section,
In order to calculate the above expectation we use the recipe
( Total_probability_rule). We consider
the disjoint situations when the process jump and does not jump. These really
are disjoint because we pass to the limit
and, thus, the Poisson process does not jump the second time with noticeable
probability.
Note, that
Prob .
The diffusion terms
in
are small compared to the jump
and do not survive the procedure
 .
Hence,
Consequently,
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