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1 results

  • Modes of growth of counting processes with increasing arrival rates

  • W. A. O'N. Waugh
  • Journal:
    Journal of Applied Probability / Volume 11 / Issue 2 / June 1974
    Published online by Cambridge University Press:
    14 July 2016, pp. 237-247
    Print publication:
    June 1974

  • Jumping processes which grow by unit jumps, with decreasing sojourn times between successive jumps, are studied. Markovian birth processes, non-Markovian branching processes, and some generalizations of these are special cases. Three classes are described, in one of which growth is explosive, in the second asymptotically continuous, and in the third oscillatory. A theorem is proved which gives an explicit functional expression in the asymptotically continuous case, and borderline cases between the classes are investigated.