Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Advances in Applied Mathematics Year : 2023

Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials

Abstract

We establish exact formulae for the persistence probabilities of an AR(1) sequence with symmetric uniform innovations in terms of certain families of polynomials, most notably a family introduced by Mallows and Riordan as enumerators of finite labeled trees when ordered by inversions. The connection of these polynomials with the volumes of certain polytopes is also discussed. Two further results provide general factorizations of AR(1) models with continuous symmetric innovations, one for negative and one for positive drift. The second factorization extends a classical universal formula of Sparre Andersen for symmetric random walks. Our results also lead to precise asymptotic estimates for the persistence probabilities.
Fichier principal
Vignette du fichier
2112.03016.pdf (502.61 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03469594 , version 1 (07-12-2021)

Identifiers

  • HAL Id : hal-03469594 , version 1

Cite

Gerold Alsmeyer, Alin Bostan, Kilian Raschel, Thomas Simon. Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials. Advances in Applied Mathematics, 2023. ⟨hal-03469594⟩
48 View
53 Download

Share

Gmail Facebook X LinkedIn More