Overview
The sum of two Ito Processes is again another Ito Process.
Given two processes
{% dX_1 = \mu_1 dt + \sigma_1 dB_1 %}
{% dX_2 = \mu_2 dt + \sigma_2 dB_2 %}
The process that results from their sum is given by
{% dX_1 + dX_2 = [\mu_1 + \mu_2 ]dt + \sqrt{[\sigma_1^2 + \sigma_2^2]} dB %}
This essentially follows from the
sum of normals.