e aim to approximate the process
given by the
SDEs
with the displaced diffusion process
Here the
,
,
,
are numbers.
are single dimensional stochastic processes.
We apply the recipes (
MarkPr1 Sigma
) and
(
MarkPr1 Beta
). Such recipes require expressions
for several expectations that we calculate
below.
The first term is zero because
and
We
continue
At this point we have expressions for the quantities of interest in terms of
and
.
We apply the operation
to the SDE for
and
obtain
The quantities of interest
are calculated above to
be
We substitute the expressions for
and calculate the
integrals:
We substitute these expressions into (
MarkPr1
Sigma
) and (
MarkPr1
Beta
):
