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Journal of Statistical Theory and Practice

, Volume 1, Issue 2, pp 227–231 | Cite as

On the Representation of Birth-Death Processes with Polynomial Transition Rates

  • Robert L. Bewernick
  • Jeremy D. Dewar
  • Eunice Gray
  • Nancy Y. Rodriguez
  • Randall J. Swift
Article

Abstract

Birth-death processes with polynomial transition rates are considered. It is shown that a deterministic population model with a polynomial growth rate corresponds to the expected population size of a birth-death process with polynomial transitions. A representation in terms of Stirling numbers, for the partial differential equation for the probability generating function of a birth-death process with polynomial transition rates is derived.

AMS Subject Classification

60J80 

Keywords

Birth-death process Stirling numbers 

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References

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Copyright information

© Grace Scientific Publishing 2007

Authors and Affiliations

  • Robert L. Bewernick
    • 1
  • Jeremy D. Dewar
    • 2
  • Eunice Gray
    • 3
  • Nancy Y. Rodriguez
    • 4
  • Randall J. Swift
    • 5
  1. 1.Department of EconomicsUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsLoyola Marymount UniversityLos AngelesUSA
  3. 3.Dept. of Mathematics & StatisticsSam Houston State UniversityHuntsvilleUSA
  4. 4.Dept. of MathematicsLoyola Marymount UniversiyLos AngelesUSA
  5. 5.Dept. of Mathematics and StatisticsCalfornia State UniversiyPomonaUSA

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