Mathematical Proceedings of the Cambridge Philosophical Society · 1955 · 587 citations · 8 references
EngineeringMathematicsProbability TheoryStochastic ModelingStochastic ProcessesContinuous-time Stochastic ProcessesMarkov ProcessesProbability DistributionsStochastic CalculusApplications To ProbabilityExponential Family DistributionsStochastic Process AnalysisStochastic Process DistributionsTransition ProbabilitiesTransition Probability Functions
ABSTRACT The exponential distribution is very important in the theory of stochastic processes with discrete states in continuous time. A. K. Erlang suggested a method of extending to other distributions methods that apply in the first instance only to exponential distributions. His idea is generalized to cover all distributions with rational Laplace transforms; this involves the formal use of complex transition probabilities. Properties of the method are considered.
8