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• 1
Book chapter
New York, NY: Springer New York
Language: English
In: Springer Series in Operations Research and Financial Engineering, An Introduction to Heavy-Tailed and Subexponential Distributions, pp.97-118
Description: In this chapter, we study a random walk whose increments have a (right) heavy-tailed distribution with a negative mean. The maximum of such a random walk is almost surely finite, and our interest is in the tail asymptotics of the distribution of this maximum, for both infinite and finite time horizons; we are further interested in the local asymptotics for the maximum in the case of an infinite time horizon. We use direct probabilistic techniques and show that, under the appropriate subexponentiality conditions, the main reason for the maximum to be far away from zero is again that a single increment of the walk is similarly large.
Keywords: Mathematics ; Probability Theory and Stochastic Processes ; Statistics for Business/Economics/Mathematical Finance/Insurance ; Statistical Physics, Dynamical Systems and Complexity ; Mathematics
ISBN: 9781441994721
ISBN: 1441994726
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• 2
Book chapter
New York, NY: Springer New York
Language: English
In: Springer Series in Operations Research and Financial Engineering, An Introduction to Heavy-Tailed and Subexponential Distributions, pp.71-96
Description: This chapter is devoted to local long-tailedness and to local subexponentiality. First we consider densities with respect to either Lebesgue measure on $$\mathbb{R}$$ or counting measure on $$\mathbb{Z}$$ . Next we study the asymptotic behaviour of the probabilities to belong to an interval of a fixed length. We give the analogues of the basic properties of the tail probabilities including two analogues of Kesten’s estimate, and provide sufficient conditions for probability distributions to have these local properties.
Keywords: Mathematics ; Probability Theory and Stochastic Processes ; Statistics for Business/Economics/Mathematical Finance/Insurance ; Statistical Physics, Dynamical Systems and Complexity ; Mathematics
ISBN: 9781441994721
ISBN: 1441994726
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• 3
Book chapter
New York, NY: Springer New York
Language: English
In: Springer Series in Operations Research and Financial Engineering, An Introduction to Heavy-Tailed and Subexponential Distributions, pp.39-69
Description: As we stated in the Introduction, all those heavy-tailed distributions likely to be of use in practical applications are not only long-tailed but possess the additional regularity property of subexponentiality. Essentially this corresponds to good tail behaviour under the operation of convolution. In this chapter, following established tradition, we introduce first subexponential distributions on the positive half-line  $${\mathbb{R}}^{+}$$ . It is not immediately obvious from the definition, but it nevertheless turns out, that subexponentiality is a tail property of a distribution. It is thus both natural, and important for many applications, to extend the concept to distributions on the entire real line  $$\mathbb{R}$$ . We also study the very useful subclass of subexponential distributions which was originally called $${\mathcal{S}}^{{_\ast}}$$ in [29] and which we name strong subexponential. In particular this class again contains all those heavy-tailed distributions likely to be encountered in practice.
Keywords: Mathematics ; Probability Theory and Stochastic Processes ; Statistics for Business/Economics/Mathematical Finance/Insurance ; Statistical Physics, Dynamical Systems and Complexity ; Mathematics
ISBN: 9781441994721
ISBN: 1441994726
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• 4
Book chapter
New York, NY: Springer New York
Language: English
In: Springer Series in Operations Research and Financial Engineering, An Introduction to Heavy-Tailed and Subexponential Distributions, pp.7-38
Description: In this chapter we are interested in (right-) tail properties of distributions, i.e. in properties of a distribution which, for any x, depend only on the restriction of the distribution to (x, ∞). More generally it is helpful to consider tail properties of functions.
Keywords: Mathematics ; Probability Theory and Stochastic Processes ; Statistics for Business/Economics/Mathematical Finance/Insurance ; Statistical Physics, Dynamical Systems and Complexity ; Mathematics
ISBN: 9781441994721
ISBN: 1441994726
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• 5
Book chapter
New York, NY: Springer New York
Language: English
In: Springer Series in Operations Research and Financial Engineering, An Introduction to Heavy-Tailed and Subexponential Distributions, pp.1-6
Description: Heavy-tailed distributions (probability measures) play a major role in the analysis of many stochastic systems. For example, they are frequently necessary to accurately model inputs to computer and communications networks, they are an essential component of the description of many risk processes, they occur naturally in models of epidemiological spread, and there is much statistical evidence for their appropriateness in physics, geoscience and economics. Important examples are Pareto distributions (and other essentially power-law distributions), lognormal distributions, and Weibull distributions (with shape parameter less than 1). Indeed most heavy-tailed distributions used in practice belong to one of these families, which are defined, along with others, in Chap. 2. We also consider the Weibull distribution at the end of this chapter.
Keywords: Mathematics ; Probability Theory and Stochastic Processes ; Statistics for Business/Economics/Mathematical Finance/Insurance ; Statistical Physics, Dynamical Systems and Complexity ; Mathematics
ISBN: 9781441994721
ISBN: 1441994726
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• 6
Book chapter
Dordrecht: Springer Netherlands
Language: English
In: Tumors of the Central Nervous System, Tumors of the Central Nervous System, Volume 8: Astrocytoma, Medulloblastoma, Retinoblastoma, Chordoma, Craniopharyngioma, Oligodendroglioma, and Ependymoma, pp.297-306
Description: Ependymoma is the third most common childhood brain tumor. The outcome of patients is still determined by the level of surgical resection and metastatic status at diagnosis, and it has not improved significantly during the past decade. The following chapter will review the molecular biology of progressively metastatizing ependymoma. Metastatic disease, which is associated with particularly poor outcome, is a rare event in ependymoma, and both magnetic resonance imaging (MRI) and cytological evaluation of cerebrospinal fluid (CSF) are important tools to diagnose primary metastases. Over the last decades, few advances have been made in terms of survival of patients with metastastatic disease, due to the lack of understanding of the molecular basis of ependymoma progression and metastasis. Emerging data suggests that genomic aberrations accumulate during progression from localized to metastatic disease. Both balanced genomic profiles as well as specific changes such as 1q gain and/or homozygous deletion of CDKN2A in primary ependymomas may predispose to secondary metastatic dissemination. However, studies of larger cohorts are urgently needed in order to identify the specific molecular mechanisms involved in primary as well as secondary metastatic spread.
Keywords: Biomedicine ; Cancer Research ; Oncology ; Pathology ; Neurosciences ; Primary Care Medicine ; Medicine
ISBN: 9789400742123
ISBN: 9400742126
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• 7
Book chapter
World Scientific Publishing Co. Pte. Ltd.
Language: English
In: Physics, Chemistry And Application Of Nanostructures : Reviews and Short Notes, 2009, pp.632-635
Description: Abstract Vacancy-related complexes which were generated in silicon p + -n diodes by irradiation with 6 MeV electrons in the temperature range of 350-800 K have been studied by means of deep level transient spectroscopy. Such defects are of interest because of their possible application in controlling the carrier lifetime in silicon power devices. Electronic parameters of defects incorporating up to three vacancies and an oxygen atom have been determined. Total introduction rate of radiation-induced defects increased about twice upon raising the irradiation temperature from 350 to 675 K.
Keywords: Nanostructure Based Devices
ISBN: 9789814280365
Source: World Scientific Books (World Scientific Publishing Co.)
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• 8
Book chapter
Language: English
Description: We present a new proof of the following fact. If =½ (log + log log + φ( )), φ( )→θ, then almost every graph with vertices and edges contains a hamiltonian cycle.
Keywords: Mathematics
ISBN: 9780444878212
ISBN: 0444878211
Source: ScienceDirect Journals (Elsevier)
Source: ScienceDirect Books (Elsevier)
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• 9
Book chapter
Elsevier Ltd
Language: English
In: Protein and Energy Supply for High Production of Milk and Meat, pp.1-14
ISBN: 978-0-08-028909-0
ISBN: 978-1-4831-1828-4
ISBN: 978-1-4831-5070-3
Source: ScienceDirect (Elsevier B.V.)
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• 10
Book chapter
Dordrecht: Springer Netherlands
Language: English
In: NATO Science Series, Nanostructured Materials by High-Pressure Severe Plastic Deformation, pp.271-274
Description: Duirng sliding friction of metals, in the surface layer (≈ 10 μ) of metals subjected to sliding friction, ultra disperse structures are formed, which to a considerable extent determine the tribological properties of the surfaces. The structures can be considered to be nanocrystalline (NC): micro-fragments with large-angle boundaries are 0.05 to 0.2 μm in size.The objects of this investigation were the nitrogen-containing Fe-Mn-(Cr) alloys (wt.%): Fe-19% Cr-10% Mn-2% Si-0.7% N-0.07% C and Fe-18% Cr-20% Mn-0.8% N-0.08% C. To compare the obtained results, we also made use of the tribological characteristics of different alloys: Fe-10% Mn-0.05% C, Fe-20% Mn-0.05% C, Fe-11% Cr-13% Mn-0.03% C, Fe-40%Mn-0.05% C and Fe-18% Cr-12% Mn-0.5% N-0.07% C, differing in phase composition, structure and the stacking fault energy (SFE). Tribological tests were done at laboratory-scale plants in conditions of sliding friction for the steel-alloy and abrasive-alloy pairs.The NC HCP ε-alloys and NC nitrogen-containing FCC γ-alloys possess low friction adhesion coefficients K and high resistance of abrasive wear ε. In these alloys, the developed basal or planar slip characterized by a smaller quantity of the slip systems condition a decrease in the resistance of NC fragments as a result of rotation and, thus, the improvement of tribological properties.Thus, the essential lowering of friction adhesion coefficient K and intensity of adhesion wear Ih, as well as the increase in the abrasive wear ε of NC HCP ε-Fe-Mn alloy and nitrogen-containing NC FCC γ-Fe-Mn-Cr alloys are mainly related to decreasing the quantity of slip systems in nanocrystals of these alloys (n → ≤3). As a result, the dislocations travel to the boundaries of nanocrystals more freely.
Keywords: Chemistry ; Materials Science ; Nanotechnology ; Metallic Materials ; Continuum Mechanics and Mechanics of Materials ; Engineering ; Chemistry
ISBN: 9781402039218
ISBN: 1402039212