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arXiv · 2004.01850

Stochastic fixed point equation and local dependence measure

Krzysztof Burdzy·Bartosz Kołodziejek·Tvrtko Tadić
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Abstract

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.

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Krzysztof Burdzy, Bartosz Kołodziejek, Tvrtko Tadić. 2020-04-04. Stochastic fixed point equation and local dependence measure. https://arxiv.org/abs/2004.01850

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