uppose
we would like to compute the quantity
given by the
relationships
where the
are real numbers,
is an integrable function and
is increment of standard Brownian motion. According to the backward
Kolmogorov's theorem, see the section
(
Backward equation section
), the
quantity
is a solution of the
problem
We introduce the process
According to the Ito formula (
Ito
formula
)
With such observation we can
write
