Statitsical fluctuations in autocatalytic reactions

The differential equations describing the statistical fluctuations of a simple autocatalytic reaction mechanism are set up and solved completely. The fluctuations are found to approach a constant limiting value when the amount of reaction product is large compared to the amount which initiates the reaction. The relative fluctuations which arise from the reaction mechanism are then equal to the reciprocal of the square root of the initial number of particles. Conversely the fluctuation in the time required to attain a threshold amount of reaction product also approaches a limiting value for high thresholds. This limiting value is greater than one time unit if the reaction is initiated by one particle, and becomes equal to one divided by the square root of the number of initiating particles if this number is large.