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Perpetuities with light tails and the local dependence measure

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  • Bihan, Julia Le
  • Kołodziejek, Bartosz

Abstract

This work investigates the tail behavior of solutions to the affine stochastic fixed-point equation of the form X=dAX+B, where X and (A,B) are independent. Focusing on the light-tail regime, following (Burdzy et al., 2022), we introduce a local dependence measure along with an associated Legendre-type transform. These tools allow us to effectively describe the logarithmic right-tail asymptotics of the solution X.

Suggested Citation

  • Bihan, Julia Le & Kołodziejek, Bartosz, 2025. "Perpetuities with light tails and the local dependence measure," Stochastic Processes and their Applications, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:spapps:v:190:y:2025:i:c:s0304414925001838
    DOI: 10.1016/j.spa.2025.104740
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