Birth-multiple catastrophe processes

Birth-multiple catastrophe processes are analyzed where the birth transition rates are assumed to be constant while catastrophes are distinguished by having possibly different destinations and possibly different transition rates. The transient probability functions of such birth-multiple catastrophe systems are determined. The solution method uses dual processes, randomization, and sample path counting. Solutions are explicit in terms of being a finite linear combination of products of exponential functions of time, t, and nonnegative integer powers of t. The coefficients within this expansion follow a pattern of rational functions of the transition rates.