Functional equations with multiple recursive terms

Ivo J.B.F. Adan; Onno J. Boxma; Jacques A.C. Resing

doi:10.1007/s11134-022-09861-9

Functional equations with multiple recursive terms

Ivo J.B.F. Adan (Corresponding author), Onno J. Boxma, Jacques A.C. Resing

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

4 Citaten (Scopus)

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In this paper, we study a functional equation for generating functions of the form
f(z) = g(z) ∑_i=1,...,M p_if(α_i(z)) + K(z), viz. a recursion with multiple recursive terms. We derive and analyze the solution of this equation for the case that the α_i(z) are commutative contraction mappings. The results are applied to a wide range of queueing, autoregressive and branching processes.

Originele taal-2	Engels
Pagina's (van-tot)	7-23
Aantal pagina's	17
Tijdschrift	Queueing Systems
Volume	102
Nummer van het tijdschrift	1-2
Vroegere onlinedatum	4 sep. 2022
DOI's	https://doi.org/10.1007/s11134-022-09861-9
Status	Gepubliceerd - okt. 2022

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abstract = "In this paper, we study a functional equation for generating functions of the form f(z) = g(z) ∑i=1,...,M pi f(αi(z)) + K(z), viz. a recursion with multiple recursive terms. We derive and analyze the solution of this equation for the case that the αi(z) are commutative contraction mappings. The results are applied to a wide range of queueing, autoregressive and branching processes.",

keywords = "Generating function, Laplace–Stieltjes transform, Queueing model, Recursion, Stochastic process",

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AU - Adan, Ivo J.B.F.

AU - Boxma, Onno J.

AU - Resing, Jacques A.C.

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N2 - In this paper, we study a functional equation for generating functions of the form f(z) = g(z) ∑i=1,...,M pi f(αi(z)) + K(z), viz. a recursion with multiple recursive terms. We derive and analyze the solution of this equation for the case that the αi(z) are commutative contraction mappings. The results are applied to a wide range of queueing, autoregressive and branching processes.

AB - In this paper, we study a functional equation for generating functions of the form f(z) = g(z) ∑i=1,...,M pi f(αi(z)) + K(z), viz. a recursion with multiple recursive terms. We derive and analyze the solution of this equation for the case that the αi(z) are commutative contraction mappings. The results are applied to a wide range of queueing, autoregressive and branching processes.

KW - Generating function

KW - Laplace–Stieltjes transform

KW - Queueing model

KW - Recursion

KW - Stochastic process

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Functional equations with multiple recursive terms

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