Stochastic fixed point equation and local dependence measure

Bartosz Ko{\l}odziejek; Krzysztof Burdzy; Tvrtko Tadi\'c

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Stochastic fixed point equation and local dependence measure

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arxiv 2004.01850 v1 pith:N55R2WJW submitted 2020-04-04 math.PR math.DS

Stochastic fixed point equation and local dependence measure

Krzysztof Burdzy , Bartosz Ko{\l}odziejek , Tvrtko Tadi\'c This is my paper

classification math.PR math.DS

keywords equationfixedpointstochasticdependencelocalmeasureanalyze

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We study solutions to the stochastic fixed point equation $X\stackrel{d}{=}AX+B$ where the coefficients $A$ and $B$ are nonnegative random variables. We introduce the ``local dependence measure'' (LDM) and its Legendre-type transform to analyze the left tail behavior of the distribution of $X$. We discuss the relationship of LDM with earlier results on the stochastic fixed point equation and we apply LDM to prove a theorem on a Fleming-Viot-type process.

Stochastic fixed point equation and local dependence measure

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