On the Limiting Proportion of Types

Mark D. Rothmann and Ralph P. Russo
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Mark D. Rothmann: Georgia Institute of Technology
Ralph P. Russo: University of Iowa

Journal of Theoretical Probability, 1997, vol. 10, issue 1, 131-143

Abstract: Abstract Consider a system into which units of random “type” enter at fixed points in time. Suppose each unit is endowed with a lifetime whose distribution is specific to its type, during which it is “active” (present in the system), and after which it is inactive (deleted from the system). Some unit types may tend to remain active for longer periods than others, and thus the limiting proportion of a given type within the active population may differ from the probability that an entering unit is of that type. The relation between the probabilities of types and the limiting proportion of types is shown to depend on the life distributions in a manner determined by the arrival time sequence.

Keywords: Continuous time process; weak limit; strong limit (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1022698532576

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