I'm having trouble finding reference material on how to deal with systems of stochastic differential equations. Specifically, I'm interested in ecological models.
For example, consider the standard Lotka-Volterra predator-prey equations: $$ \begin{aligned} \frac{dx}{dt}&=rx-\gamma xy \\ \frac{dy}{dt}&=\alpha xy-my. \end{aligned} $$
I'd like to study stochastic versions of this and similar models. Something like:
$$ \begin{aligned} dX&=(rX-\gamma XY)dt+c_1XdB \\ dY&=(\alpha XY-mY)dt+c_2YdB. \end{aligned} $$
Is the above SDE system sensible/tractable? I'm sure basic stochastic predator-prey models have been beat to death already, but I just can't find them (or my inability to understand them may be the issue).
Any insight, hints, or references is appreciated. Right now I'm reading Stochastic Differential Equations by Bernt Øksendal (in chapter 3 so far). Will this text give me what I need, or are there other texts that will help with systems such as the above?