A use of complex probabilities in the theory of stochastic processes
Использование комплексных вероятностей в теории стохастических процессов
1955-04-01
SCID: 54.1/dbuqgnjt
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Erlang methodcomplex transition probabilitiesexponential distributionrational Laplace transformsstochastic processes
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Abstract (AI)
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.
Key Findings
1
The generalization formally introduces complex transition probabilities into the theory of stochastic processes with discrete states in continuous time.
2
The method’s properties are analyzed, establishing how complex-probability techniques can extend standard exponential-distribution approaches.
3
The paper generalizes Erlang’s method from exponential distributions to all distributions with rational Laplace transforms.
4
The work addresses an important limitation of conventional stochastic-process methods, which initially apply only to exponential waiting-time distributions.
Research Object
stochastic processes with discrete states in continuous time
Research Subject
generalization of Erlang’s method to distributions with rational Laplace transforms using formal complex transition probabilities
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1955-04-01
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