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A one-dimensional birth and death process in random environment

  • Kiyoshi Kawazu
Article

Abstract

To each integern, a random variableη n is attached at the integer point {n} andλ n is attached at the interval (n, n+1) as random environment. We give the global limit theorem of one dimensional birth and death processes in these random media, that is, preparing two independent ratesg(n) andh(n) which are induced by λ’s and η’s, respectively, we prove that the process {X(g(n)h(n)t)/n} converges to a continuous self-similar process.

Key words

random environment birth and death process Brownian motion J1-convergence 

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Copyright information

© JJAM Publishing Committee 1989

Authors and Affiliations

  • Kiyoshi Kawazu
    • 1
  1. 1.Department of Mathematics, Faculty of EducationYamaguchi UniversityYamaguchiJapan

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