Fixed points of inhomogeneous smoothing transforms

@article{Alsmeyer2012FixedPO,
  title={Fixed points of inhomogeneous smoothing transforms},
  author={Gerold Alsmeyer and Matthias Meiners},
  journal={Journal of Difference Equations and Applications},
  year={2012},
  volume={18},
  pages={1287 - 1304}
}
We consider the inhomogeneous version of the fixed-point equation of the smoothing transformation, that is, the equation , where means equality in distribution, is a given sequence of non-negative random variables and is a sequence of i.i.d. copies of the non-negative random variable X independent of . In this situation, X (or, more precisely, the distribution of X) is said to be a fixed point of the (inhomogeneous) smoothing transform. In the present paper, we give a necessary and sufficient… 
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