This is somewhat of a high-level, I-hardly-know-much-about-the-topic-yet question, but here goes.
I came across online a presentation in which part of it documented deriving an SDE for a population dynamics system between two different groups. In it, the author creates a matrix, $B$, which is another matrix, $V^{\frac{1}{2}}$. See (http://www.nimbios.org/tutorials/TT_stochastic_modeling_talks/eallenUTlect1.pdf, Slide 63)
If I had a system of THREE populations that are very similar to the situation presented in this presentation, would I need to take the cube root of my derived matrix, $V$?
Apologies if this has little appearance of background research -- I haven't encountered SDEs academically but am trying to derive an analog to a discrete-time system of equations and a Monte Carlo simulation I'm working on.