 Symmetric stochastic attrition process

This finite-state Markov jump process models two opposing populations, each suffering losses at a rate proportional to the surviving opposing population. Both coordinate axes are absorbing. Its embedded jump chain removes one individual at each step, with probabilities $b/(a+b)$ and $a/(a+b)$. The corresponding deterministic equations $\dot{a}=-\kappa b$, $\dot{b}=-\kappa a$ conserve $a^2-b^2$; finite stochastic populations satisfy a near-invariant instead.