Fourier Analysis of Semistable Distributions

Csörgő, Sándor

doi:10.1007/s10440-007-9143-9

Cited by 5 publications

(7 citation statements)

References 13 publications

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“…Also, B kn is such that lim r→∞ B kn /k n exists. For the form and properties of the characteristic function of the random variable V we refer to [26,9].…”

Section: Methods Of Proof and The Main Dynamical Ingredientmentioning

confidence: 99%

“…Since X 1 satisfies (H3), [26, Theorem 1] (see also [9,Lemma 1]) ensures that there exist C 2 > C 1 > 0 such that C 1 s β (1/s) ≤G(s) + sE P (X 1 ) ≤ C 2 s β (1/s); the analysis in [26,9] is in terms of Fourier transforms and carries over with simplified arguments to real Laplace transforms, as required forG(s). In particular, given…”

Section: It Remains To Estimate G(s) By (H0) and (H3mentioning

confidence: 99%

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Limit theorems for wobbly interval intermittent maps

2021

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We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general Hölder observables fail. We obtain limit laws for such maps and Hölder observables. These limit laws are similar to the classical semistable laws previously established for random processes. One of the examples considered is an interval map with a countable number of discontinuities, and to analyse it we need to construct a Markov/Young tower.

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“…Also, B kn is such that lim r→∞ B kn /k n exists. For the form and properties of the characteristic function of the random variable V we refer to [26,9].…”

Section: Methods Of Proof and The Main Dynamical Ingredientmentioning

confidence: 99%

Section: It Remains To Estimate G(s) By (H0) and (H3mentioning

confidence: 99%

Limit theorems for wobbly interval intermittent maps

2021

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“…Therefore I 3 ≤ 2πA n a n , while ψ γn (t) is uniformly integrable by ( 7) in [7], implying lim K→∞ I 4 = 0.…”

Section: Local Limit Theoremsmentioning

confidence: 98%

Strong renewal theorem and local limit theorem in the absence of regular variation

Kevei¹,

Terhesiu²

2020

Preprint

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We obtain a strong renewal theorem with infinite mean beyond regular variation, when the underlying distribution belongs to the domain of geometric partial attraction a semistable law with index α ∈ (1/2, 1]. In the process we obtain local limit theorems for both finite and infinite mean, that is for the whole range α ∈ (0, 2). We also derive the aymptotics of the renewal function for α ∈ (0, 1].

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“…Without loss of generality we may assume that A n = n 1/β ℓ 1 (n), β ∈ (0, 2), with some slowly varying function ℓ 1 (see [28,Theorem 3]). For the form and properties of the characteristic function of the random variable V we refer to [26,10].…”

Section: General Background On Semistable Lawsmentioning

confidence: 99%

“…Since X 1 satisfies (H3), [26, Theorem 1] (see also [10,Lemma 1]) ensures that there exist [26,10] is in terms of Fourier transforms and carries over with simplified arguments to real Laplace transforms, as required for G(s). In particular, given C 0 := inf x>0 M (x) > 0, we have…”

Section: Transfer Operators For F F and F ∆mentioning

confidence: 99%

Limit theorems for wobbly interval intermittent maps

Coates¹,

Holland²,

Terhesiu³

2019

Preprint

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We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general Hölder observables fail. We obtain limit laws for such maps and Hölder observables. These limit laws are similar to the classical semistable laws previously established for deterministic processes, but certain limitations imposed by the current dynamical setup are reflected in the main result. One of the considered examples is an interval map with a countable number of discontinuities, and to analyse it we need to construct a Markov/Young tower.

show abstract

Fourier Analysis of Semistable Distributions

Cited by 5 publications

References 13 publications

Limit theorems for wobbly interval intermittent maps

Limit theorems for wobbly interval intermittent maps

Strong renewal theorem and local limit theorem in the absence of regular variation

Limit theorems for wobbly interval intermittent maps

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