Limit theorems for a higher order time dependent Markov chain model

• Autorzy: Kokoszka Piotr , Kutta Tim , Singh Deepak , Wang Haonan
• Języki publikacji: EN

Abstrakty

EN

The paper establishes a strong law of large numbers and a central limit theorem for a sequence of dependent Bernoulli random variables modeled as a higher order Markov chain. The model under consideration is motivated by problems in quality control where acceptability of an item depends on the past k acceptability scores. Moreover, the model introduces dependence that may evolve over time and thus advances the theory for models with time invariant dependence. We establish explicit assumptions that incorporate this dynamic dependence and show how it enters into the limits describing long-term behavior of the system.

Słowa kluczowe

EN

central limit theorem; dependent Bernoulli observations; higher order Markov model; strong law of large numbers

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2023
• Tom: Vol. 43, Fasc. 1
• Strony: 121--139
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Kokoszka Piotr

• Department of Statistics, Colorado State University, Fort Collins, CO 80521, USA

autor

Kutta Tim

• Department of Statistics, Colorado State University, Fort Collins, CO 80521, USA

autor

Singh Deepak

• Department of Statistics, Colorado State University, Fort Collins, CO 80521, USA

autor

Wang Haonan

• Department of Mathematics, Indian Institute of Technology, Ropar Bara Phool, Punjab 140001, India

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).