Neighborhood Unions and Z 3-Connectivity in Graphs

Li, Liangchen; Li, Xiangwen

doi:10.1007/s00373-012-1240-5

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…Since E(Y 0 ) < ∞ and the moment condition R\{0} |z|½ {|z| 1} ν(dz) < ∞ trivially holds, we may apply formula (3.1.11) in Li [27] or Lemma 3.4 and (2.14) in Barczy et al [5] with…”

Section: Preliminariesmentioning

confidence: 99%

Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations

et al. 2019

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We consider a stable Cox-Ingersoll-Ross process driven by a standard Wiener process and a spectrally positive strictly stable Lévy process, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate based on continuous time observations. We distinguish three cases: subcritical, critical and supercritical. In all cases we prove strong consistency of the MLE in question, in the subcritical case asymptotic normality, and in the supercritical case asymptotic mixed normality are shown as well. In the critical case the description of the asymptotic behavior of the MLE in question remains open.

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“…Since E(Y 0 ) < ∞ and the moment condition R\{0} |z|½ {|z| 1} ν(dz) < ∞ trivially holds, we may apply formula (3.1.11) in Li [27] or Lemma 3.4 and (2.14) in Barczy et al [5] with…”

Section: Preliminariesmentioning

confidence: 99%

Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations

et al. 2019

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“…2)), we may apply formula (3.1.11) in Li [34] or Lemma 3.4 in Barczy et al [5] with the choices B = B = −b and…”

Section: Preliminariesmentioning

confidence: 99%

Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations

Barczy

Alaya

Kebaier

et al. 2018

Stochastic Processes and their Applications

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We consider a jump-type Cox-Ingersoll-Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical and supercritical. In the subcritical case we prove weak consistency and asymptotic normality, and, under an additional moment assumption, strong consistency as well. In the supercritical case, we prove strong consistency and mixed normal (but non-normal) asymptotic behavior, while in the critical case, weak consistency and non-standard asymptotic behavior are described. We specialize our results to socalled basic affine jump-diffusions as well. Concerning the asymptotic behavior of the MLE in the supercritical case, we derive a stochastic representation of the limiting mixed normal distribution, where the almost sure limit of an appropriately scaled jump-type supercritical CIR process comes into play. This is a new phenomenon, compared to the critical case, where a diffusion-type critical CIR process plays a role.

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Nowhere-zero 3-flows and Z3-connectivity of graphs without two forbidden subgraphs

Liu

2016

Discrete Mathematics

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Neighborhood Unions and Z 3-Connectivity in Graphs

Cited by 3 publications

References 14 publications

Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations

Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations

Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations

Nowhere-zero 3-flows and Z3-connectivity of graphs without two forbidden subgraphs

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