Abstract
We study solutions to the stochastic fixed-point equation 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.
Funding Statement
Research of the first author was supported in part by Simons Foundation Grant 506732.
Acknowledgments
We are grateful to the referees for many suggestions for improvement.
The third author would like to thank the Department of Mathematics at the University of Washington in Seattle, where the project took place, for the hospitality. The third author is also grateful to the Microsoft Corporation for allowance on Azure cloud service where he ran many simulations.
Citation
Krzysztof Burdzy. Bartosz Kołodziejek. Tvrtko Tadić. "Stochastic fixed-point equation and local dependence measure." Ann. Appl. Probab. 32 (4) 2811 - 2840, August 2022. https://doi.org/10.1214/21-AAP1749
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