Treatment of the background error in the statistical analysis of Poisson processes

The formalism that allows one to take into account the error sigma(b) of the expected mean background (b) over bar in the statistical analysis of a Poisson process with the frequentistic method is presented. It is shown that the error sigma(b) cannot be neglected if it is not much smaller than root (b) over bar. The resulting confidence belt is larger that the one for sigma(b)=0, leading to larger confidence intervals for the mean mu of signal events. [S0556-2821(99)03211-7].