e consider the original
SDE
and a perturbed
SDE
We introduce the
difference
The difference
is given by the following
SDE
We assume that the functions
and
are such that the solution of the original SDE
changes slightly when the perturbation of the initial condition is slight.
Hence, the
is small if
is small.
Consequently,
We substitute these approximations into the SDE for
and note that such SDE scales with the magnitude of
.
We introduce the process
:
We arrive to the following system of
SDEs:
The derivative of interest may be expressed in terms of
and
:
