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2 results

  • Renewal processes decomposable into i.i.d. components

  • Yoshifusa Ito
  • Journal:
    Advances in Applied Probability / Volume 12 / Issue 3 / September 1980
    Published online by Cambridge University Press:
    01 July 2016, pp. 672-688
    Print publication:
    September 1980

  • Let N be a stationary renewal process with a probability density function f(t). Suppose that N can be expressed as the superposition of a finite number of i.i.d. stationary components N(1), …, N(p) (p≧2). Then, under a supplementary condition on f(t), N and N(1), …, N(p) are all Poisson. This is proved by using recurrence relations given in Ito (1978) for the probability distribution of i.i.d. components of a superposition process.

  • Superposition and decomposition of stationary point processes

  • Yoshifusa Ito
  • Journal:
    Journal of Applied Probability / Volume 15 / Issue 3 / September 1978
    Published online by Cambridge University Press:
    14 July 2016, pp. 481-493
    Print publication:
    September 1978

  • A recursion formula is obtained by rearranging Lawrance's (1973) result concerning the superposition of independent stationary point processes for which there exist joint probability density functions for the intervals between successive points. When these component point processes are identically distributed, the formula can in principle be inverted to describe their probability structure given that of the superposition process.