Large Time Asymptotic of Heavy Tailed Renewal Processes

Horii, Hiroshi; Lefevere, R.; Nemoto, Takahiro

doi:10.1007/s10955-021-02856-5

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A a Counting Process With Smaller Power-law Exponents1

Introduction1

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2022

2023

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Cited by 3 publications

(2 citation statements)

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“…For the counting process with a general fat tail waiting time distribution (that has a power law decay as t → ∞), an existence of the affine part in the scaled cumulant generating function (sCGF) G(s) = lim t→∞ (1/t) ln E[e sNt ] has been proven [16]. When the sCGF is analytic, it can be expanded using scaled cumulants ci (i = 1, 2, ...) as G(s) = ∞ i=1 (c i /i!…”

Section: A a Counting Process With Smaller Power-law Exponentsmentioning

confidence: 99%

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Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions

Horii¹,

Lefevere²,

Itami³

et al. 2022

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Section: A a Counting Process With Smaller Power-law Exponentsmentioning

confidence: 99%

“…But he used a condition in which an affine part can not be present. Recently, in [16], the authors studied finite-time corrections of the moment generating function under the condition that the affine part appears (Theorem 2.1). Yet they did not succeed to translate it to the correction term of the LDP.…”

Section: Introductionmentioning

confidence: 99%