First-Order Stochastic Processes

A general class of ``first-order'' stochastic processes is defined as those for which the probability per unit time of a transition out of a state is proportional to the occupancy of that state. The solution to the differential-difference equation for the process, obtained earlier by Siege...

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Bibliographic Details
Published in:The Journal of chemical physics 1960-01, Vol.32 (1), p.247-250
Main Authors: Krieger, Irvin M., Gans, Paul J.
Format: Article
Language:English
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Summary:A general class of ``first-order'' stochastic processes is defined as those for which the probability per unit time of a transition out of a state is proportional to the occupancy of that state. The solution to the differential-difference equation for the process, obtained earlier by Siegert [Phys. Rev. 76, 1708 (1949)], is obtained here using more elementary mathematics. The resultant solution is used to demonstrate that a system relaxing by first-order processes from one equilibrium state to another will maintain, at all times, a multinomial distribution.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.1700909