n
the formula ( Change of Brownian
motion) the
and
are columns and the
 are
scalar products. We intend to apply the result
( Change of Brownian motion) to a
situation of two assets given by one dimensional correlated diffusion
terms. 
where the expression
stands for
 's
Brownian motion with respect to
taken as numeraire. We assume
that
for some number
 .
We are seeking a matrix
 such
that
where
is a column of independent standard Brownian motions.
Observe that the Brownian motions
given
by
are standard and satisfy the
condition
Hence, it is enough to set
We write
 
The formula ( Change of Brownian
motion) takes the
form
Therefore, we write SDE for
in the
 -measure
as
follows 
where the Brownian motions
 are
standard under the measure of numeraire
and satisfy the
relationship
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