A use of complex probabilities in the theory of stochastic processes
Mathematical Proceedings of the Cambridge Philosophical Society · 1955 · 585 citations · 8 references
Stochastic ProgrammingRational Laplace TransformsExponential DistributionEngineeringDiscrete ProbabilityNatural SciencesStochastic ProcessesMarkov ProcessesStochastic CalculusExponential DistributionsStochastic Dynamical SystemStochastic SystemLevy ProcessProbability TheoryStochastic PhenomenonComplex ProbabilitiesDecision TheoryStatistics
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.
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An introduction to probability theory and its applications
Journal of the Franklin Institute · 1958
Discrete ProbabilityProbability TheoryProbabilistic Analysis+1
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