= Addition law for square-root branching diffusions
{title2=$Z+Z'\text{ starts at }z+z'$}
For solutions with independent Brownian drivers in a common filtration, combine the drivers with weights $\sqrt{Z/(Z+Z')}$ and $\sqrt{Z'/(Z+Z')}$ where the sum is positive. At zero use one original driver. The resulting continuous <local martingale> has bracket $t$ and is <Brownian motion> by the <Lévy characterization of Brownian motion>. Multiplying its differential by $\sqrt{Z+Z'}$ gives exactly the sum of the original stochastic differentials.
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