For example, consider the (linear) chemical system involving two chemical species  and  and the reaction . In this system,  (species),  (reactions). A state of the system is a vector , where  are the number of molecules of  and  respectively. Let , so that the rate of reaction 1 (the only reaction) depends on the concentration of . The stoichiometry matrix is .
Then the master equation reads:
where  is the shift caused by the action of the product of step operators, required to change state  to a precursor state .