Limit Theorems for A Degenerate Fixed Point Equation †
نویسندگان
چکیده
We consider the stochastic fixed point equation Xn d = Xn−D +B that appears in several applications, for example in the Bolthausen-Sznitman coalescent or in the analysis or recursive algorithms. In this paper we provide a systematic study on these kinds of stochastic fixed point equations. It turns out that depending on the singularity structure of the the moment generating function of D the limiting distribution is either a Mittag-Leffler distribution, a normal distribution, or a spectrally negative stable distribution with index of stability 1.
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