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A Note on the Approximation of Perpetuities

Abstract : We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the perpetuity. We significantly reduce the complexity of the earlier algorithm. Also one particular perpetuity arising in the analysis of the selection algorithm Quickselect is studied in more detail. Our approach works well for distribution functions. For densities we have weaker error bounds although computer experiments indicate that densities can also be well approximated.
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Margarete Knape, Ralph Neininger. A Note on the Approximation of Perpetuities. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. pp.123-136, ⟨10.46298/dmtcs.3544⟩. ⟨hal-01184792⟩

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