e use technique of the previous section to calculate the operator
(
Backward Kolmogorov generator
)
for the
process
where the Poisson process
has the intensity
and
is conditionally independent from
.
Similarly to the previous
section,
In order to calculate the above expectation we use the recipe
(
Total_probability_rule
). We consider
the disjoint events
the
process
does not jump during
,
the
process
jumps once during
and
.
.
According to the chapter (
Poisson
process
),
By the conditional independence of
and
,
the diffusion terms
in
are small compared to the jump
and do not survive the procedure
.
Hence,
In
addition,
Consequently,
The above results agrees with the section
(
Backward_equation_for_jump_diffusion
).
