Exercise $1.$

Variables $x_1$ and $x_2$ follow generalized Wiener processes with drift rates ${}_1$ and ${}_2$ and variances ${}_1^2$ and ${}_2^2.$ What process does $x_1+x_2$ follow if:

$($a$)$ The changes in $x_1$ and $x_2$ in any short interval of time are uncorrelated?

$($b$)$ There is a correlation $$ between the changes in and in any short interval of time?