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Probability enters state $n$ through a birth from $n-1$ or a pair-death event from $n+2$, and leaves through either event at state $n$. Thus the Kramers-Moyal master equation iswith probabilities and impossible transition rates taken as zero outside the nonnegative states.

A birth changes $n$ by $+1$, while a death event changes it by $-2$. Applying these increments to the first moment givesConsequently every steady state must satisfy

For jump rate $W(n,r)$ from $n$ to $n+r$, probability enters state $n$ from $n-r$ and leaves it from $n$. The resulting kramers-Moyal master equation is