= Symmetric stochastic attrition process
{title2=$(a,b)\to(a-1,b)\text{ at rate }\kappa b,\quad(a,b)\to(a,b-1)\text{ at rate }\kappa a$}
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.
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