具有轻尾的永续与局部依赖测度

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-07-17 DOI:10.1016/j.spa.2025.104740

Julia Le Bihan, Bartosz Kołodziejek

引用次数: 0

摘要

本文研究了形式为X=dAX+B的仿射随机不动点方程解的尾部行为，其中X和（A，B）是独立的。关注光尾状态，接下来（burzy et al., 2022），我们引入了一个局部依赖度量以及相关的legende型变换。这些工具使我们能够有效地描述解x的对数右尾渐近性。此外，我们将分析扩展到相关的递归序列Xn=AnXn−1+Bn，其中（An,Bn）n是（a，B）的iid个副本。对于这个序列，我们构造了确定性标度（fn）n，使得lim supn→∞Xn/fn是正有限的，并给出了它的非随机显式值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Perpetuities with light tails and the local dependence measure

This work investigates the tail behavior of solutions to the affine stochastic fixed-point equation of the form

X \overset{d}{=} A X + 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

Moreover, we extend our analysis to a related recursive sequence

X_{n} = A_{n} X_{n - 1} + B_{n}

, where

{(A_{n}, B_{n})}_{n}

are i.i.d. copies of

(A, B)

. For this sequence, we construct deterministic scaling

{(f_{n})}_{n}

such that

{lim sup}_{n \to \infty} X_{n} / f_{n}

is a.s. positive and finite, with its non-random explicit value provided.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.