Iterated ergodic theorems and Erdös–Rényi law of large numbers

Yuri Kifer

doi:10.1016/j.spl.2025.110572

Iterated ergodic theorems and Erdös–Rényi law of large numbers

Yuri Kifer

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We obtain ergodic theorems and a version of the Erdös–Rènyi law of large numbers for multiple iterated sums and integrals of the form Σ^(ν)(t)=∑_{0≤k₁<…<k_ν≤t}ξ(k₁)⊗⋯⊗ξ(k_ν), t∈[0,T] and Σ^(ν)(t)=∫_{0≤s₁≤⋯≤s_ν≤t}ξ(s₁)⊗⋯⊗ξ(s_ν)ds₁⋯ds_ν where {ξ(k)}_−∞<k<∞ and {ξ(s)}_−∞<s<∞ are stationary vector stochastic processes.

Original language	English
Article number	110572
Journal	Statistics and Probability Letters
Volume	228
DOIs	https://doi.org/10.1016/j.spl.2025.110572
State	Published - Feb 2026

Bibliographical note

Publisher Copyright:
© 2025 Elsevier B.V.

Keywords

Dynamical systems
Ergodic theorems
Iterated sums and integrals
Stationary processes

Access to Document

10.1016/j.spl.2025.110572

Cite this

@article{b94481f1e5464ce18807147dfd62f2e9,

title = "Iterated ergodic theorems and Erd{\"o}s–R{\'e}nyi law of large numbers",

abstract = "We obtain ergodic theorems and a version of the Erd{\"o}s–R{\`e}nyi law of large numbers for multiple iterated sums and integrals of the form Σ(ν)(t)=∑0≤k1<…ν≤tξ(k1)⊗⋯⊗ξ(kν), t∈[0,T] and Σ(ν)(t)=∫0≤s1≤⋯≤sν≤tξ(s1)⊗⋯⊗ξ(sν)ds1⋯dsν where \{ξ(k)\}−∞ and \{ξ(s)\}−∞ are stationary vector stochastic processes.",

keywords = "Dynamical systems, Ergodic theorems, Iterated sums and integrals, Stationary processes",

author = "Yuri Kifer",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier B.V.",

year = "2026",

month = feb,

doi = "10.1016/j.spl.2025.110572",

language = "אנגלית",

volume = "228",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Iterated ergodic theorems and Erdös–Rényi law of large numbers

AU - Kifer, Yuri

PY - 2026/2

Y1 - 2026/2

N2 - We obtain ergodic theorems and a version of the Erdös–Rènyi law of large numbers for multiple iterated sums and integrals of the form Σ(ν)(t)=∑0≤k1<…ν≤tξ(k1)⊗⋯⊗ξ(kν), t∈[0,T] and Σ(ν)(t)=∫0≤s1≤⋯≤sν≤tξ(s1)⊗⋯⊗ξ(sν)ds1⋯dsν where {ξ(k)}−∞ and {ξ(s)}−∞ are stationary vector stochastic processes.

AB - We obtain ergodic theorems and a version of the Erdös–Rènyi law of large numbers for multiple iterated sums and integrals of the form Σ(ν)(t)=∑0≤k1<…ν≤tξ(k1)⊗⋯⊗ξ(kν), t∈[0,T] and Σ(ν)(t)=∫0≤s1≤⋯≤sν≤tξ(s1)⊗⋯⊗ξ(sν)ds1⋯dsν where {ξ(k)}−∞ and {ξ(s)}−∞ are stationary vector stochastic processes.

KW - Dynamical systems

KW - Ergodic theorems

KW - Iterated sums and integrals

KW - Stationary processes

UR - https://www.scopus.com/pages/publications/105017540010

U2 - 10.1016/j.spl.2025.110572

DO - 10.1016/j.spl.2025.110572

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:105017540010

SN - 0167-7152

VL - 228

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 110572

ER -

Iterated ergodic theorems and Erdös–Rényi law of large numbers

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this