Analytic solution of the chemical master equation

Consider a spatially homogeneous system of volume V. Suppose the simple reaction is taking place in the system, where species Si decomposes irreversibly to species S2 and S3, 

If there are X1 molecules of species Si in volume V at time t, define 

It turns out that constant ci is equal to the kinetic reaction constant 1 in this simple case. Let us prove this. 

By definition, the kinetic constant ki is the average reaction rate per unit volume divided by the concentration of 5i, 

Cp dt = average probability that a particular combination of reactant molecules will react according to in the next infinitesimal time interval dt. (13.23) 

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