| Summary: | 碩士 === 國立中山大學 === 應用數學研究所 === 85 ===
Let {N(t),t≧0} be a renewal process. For each n≧1, assume we have a sequence of random variables {xni, i≧1}, which only take values 0 and 1 and satisfies the following two conditions: (a) {Xni,i≧1} is independent of the renewal process {N(t),t≧0} , (b) there exists a random variable {Yn, n≧1} , with 0<Yn<1, Vn≧1, such that conditional on Yn, {Xni,i≧1} are i.i.d. Bernoulli random variables. Let Nn(t) = Σi=1 Xni. Under certain conditions we prove that {Nn(t), t≧0} converges in distribution to a Poisson process.
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