Note on the stochastic theory of a self-catalytic chemical reaction. I

By using the spectral theory of the master equation, it is shown generally that a self-catalytic chemical system may evolve according to two widely different time scales in this case. The shorter one describes the evolution towards a quasi-stationary state which is the stochastic equivalent of the macroscopic stationary state. The larger time characterizes the final evolution towards total absorption; it is coarsely evaluated for an arbitrary system and more precisely for a non step-by-step reaction. Detailed application to step-by-step reactions is given in a second article.