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Absolute continuity of one-sided random translations

Author

Listed:
  • Sato, Hiroshi
  • Tamashiro, Masakazu

Abstract

Let X = Xkk [greater-or-equal, slanted] 1 be an i.i.d. random sequence and Y =Ykk [greater-or-equal, slanted] 1 be an independent random sequence which is also independent of X. We suppose X and Y take values in the sequence space , where S is either , the space of non-negative integers, or +, the space of non-negative numbers. Then X and X + Y = Xk + Ykk [greater-or-equal, slanted] 1 induce probability measures [mu]X and [mu]X + Y on SN, respectively. We shall give necessary or sufficient conditions for [mu]X ~ [mu]X + Y (equivalence = mutual absolute continuity) under assumptions on the distribution of X1. In particular, we consider the case where X1 obeys a Poisson or an exponential law.

Suggested Citation

  • Sato, Hiroshi & Tamashiro, Masakazu, 1995. "Absolute continuity of one-sided random translations," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 187-204, August.
    • Handle: RePEc:eee:spapps:v:58:y:1995:i:2:p:187-204
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