Fixed points of a generalized smoothing transformation and applications to the branching random walk

@inproceedings{Liu1998FixedPO,
  title={Fixed points of a generalized smoothing transformation and applications to the branching random walk},
  author={Quansheng Liu},
  year={1998}
}
Let {Ai: i > 11 be a sequence of non-negative random variables and let M be the class of all probability measures on [0, oo]. Define a transformation T on M by letting T,i be the distribution of A?1 AiZi, where the Zi are independent random variables with distribution i, which are also independent of {Ai}. Under first moment assumptions imposed on {Ai}, we determine exactly when T has a non-trivial fixed point (of finite or infinite mean) and we prove that all fixed points have regular… CONTINUE READING

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