A Markov branching process is considered where particles may be subject to capture and multiplicative reactions. In the case of constant capture and multiplicative reaction probabilities the author gives in closed form expressions for the probability generating functions of the number of existing particles at any fixed time and the number of detector counted particles in the medium during a time interval.
In a similar way the probability generating functions are given for the case when a random source produces particles which themselves can produce branches with different origins. Also the conditional probabilities are computed that n particles are found or counted, respectively, at time \(t>0\) after we have found m particles or counted at \(t=0\). The results are then applied to binary splitting.