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1 results

  • Birth-death processes with an instantaneous reflection barrier

  • Part of
  • Anyue Chen, Kai Liu
  • Journal:
    Journal of Applied Probability / Volume 40 / Issue 1 / March 2003
    Published online by Cambridge University Press:
    14 July 2016, pp. 163-179
    Print publication:
    March 2003

  • A new structure with the special property that an instantaneous reflection barrier is imposed on the ordinary birth—death processes is considered. An easy-checking criterion for the existence of such Markov processes is first obtained. The uniqueness criterion is then established. In the nonunique case, all the honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. It is proved that honest processes are always ergodic without necessarily imposing any extra conditions. Equilibrium distributions for all these ergodic processes are established. Several examples are provided to illustrate our results.