scholarly journals Large deviations of means of heavy-tailed random variables with finite moments of all orders

2017 ◽  
Vol 54 (1) ◽  
pp. 66-81
Author(s):  
Jaakko Lehtomaa
Keyword(s):  
Large Deviations ◽  
Hazard Function ◽  
The Novel ◽  
Exponential Distributions ◽  
Large Deviations Principle ◽  
Novel Approach ◽  
Logarithmic Asymptotics ◽  
The Mean ◽  
Heavy Tailed ◽  
Finite Moments

AbstractLogarithmic asymptotics of the mean process {Sn∕n} are investigated in the presence of heavy-tailed increments. As a consequence, a full large deviations principle for means is obtained when the hazard function of an increment is regularly varying with index α∈(0,1). This class includes all stretched exponential distributions. Thus, the previous research of Gantert et al. (2014) is extended. Furthermore, the presented proofs are more transparent than the techniques used by Nagaev (1979). In addition, the novel approach is compatible with other common classes of distributions, e.g. those of lognormal type.

scholarly journals Large Deviations for a Class of Multivariate Heavy-Tailed Risk Processes Used in Insurance and Finance

2021 ◽  
Vol 14 (5) ◽  
pp. 202
Author(s):  
Miriam Hägele ◽  
Jaakko Lehtomaa
Keyword(s):  
Large Deviations ◽  
Risk Sharing ◽  
Dependence Structure ◽  
Large Deviations Principle ◽  
Shape Constraint ◽  
Multiple Components ◽  
Insurance Portfolio ◽  
Heavy Tailed ◽  
Tail Events ◽  
Risk Processes

Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the main problems is to decide if there is any type of dependence between the components of the vector and, if so, what type of dependence structure should be used for accurate modelling. We study a class of heavy-tailed multivariate random vectors under a non-parametric shape constraint on the tail decay rate. This class contains, for instance, elliptical distributions whose tail is in the intermediate heavy-tailed regime, which includes Weibull and lognormal type tails. The study derives asymptotic approximations for tail events of random walks. Consequently, a full large deviations principle is obtained under, essentially, minimal assumptions. As an application, an optimisation method for a large class of Quota Share (QS) risk sharing schemes used in insurance and finance is obtained.

scholarly journals Solutions for the Cahn—Hilliard equation with many boundary spike layers

2001 ◽  
Vol 131 (1) ◽  
pp. 185-204 ◽  
Author(s):  
Juncheng Wei ◽  
Matthias Winter
Keyword(s):  
Positive Integer ◽  
Mean Curvature ◽  
Local Minimum ◽  
Stationary Solutions ◽  
The Novel ◽  
Hilliard Equation ◽  
Local Minimum Point ◽  
Novel Approach ◽  
The Mean ◽  
Cahn Hilliard Equation

In this paper we construct new classes of stationary solutions for the Cahn–Hilliard equation by a novel approach.One of the results is as follows. Given a positive integer K and a (not necessarily non-degenerate) local minimum point of the mean curvature of the boundary, then there are boundary K-spike solutions whose peaks all approach this point. This implies that for any smooth and bounded domain there exist boundary K-spike solutions.The central ingredient of our analysis is the novel derivation and exploitation of a reduction of the energy to finite dimensions (lemma 3.5), where the variables are closely related to the peak locations.

scholarly journals Large deviations for the empirical measure of heavy-tailed Markov renewal processes

2016 ◽  
Vol 48 (3) ◽  
pp. 648-671 ◽  
Author(s):  
Mauro Mariani ◽  
Lorenzo Zambotti
Keyword(s):  
Large Deviations ◽  
Finite Graph ◽  
Rate Function ◽  
Empirical Measure ◽  
Markov Renewal Process ◽  
Large Deviations Principle ◽  
Arrival Times ◽  
Heavy Tailed Distributions ◽  
Markov Renewal Processes ◽  
Heavy Tailed

Abstract A large deviations principle is established for the joint law of the empirical measure and the flow measure of a Markov renewal process on a finite graph. We do not assume any bound on the arrival times, allowing heavy-tailed distributions. In particular, the rate function is in general degenerate (it has a nontrivial set of zeros) and not strictly convex. These features show a behaviour highly different from what one may guess with a heuristic Donsker‒Varadhan analysis of the problem.

System and Method for Investigating Arterial Remodeling

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
Alexander Rachev ◽  
Zachary Dominguez ◽  
Raymond Vito
Keyword(s):  
Organ Culture ◽  
Mechanical Response ◽  
Circumferential Stress ◽  
The Novel ◽  
Mechanical Parameters ◽  
Pressure Flow ◽  
Novel Approach ◽  
Baseline Values ◽  
The Mean ◽  
Porcine Carotid Artery

Organ culture systems are used to study remodeling of arteries and to fabricate tissue engineered vascular grafts. Investigations to date focused on changes in geometry and mechanical response of arteries or constructs associated with controlled sustained alterations in the global load parameters such as the arterial pressure, flow, or axial stretch. A new experimental paradigm is proposed, which is based on the simultaneous independent control of local mechanical parameters such as mean strain or stress in the arterial wall and flow-induced shear at the intima. An organ culture system and methodology were developed, which controls pressure, flow, and axial length of a specimen in order to maintain the local mechanical parameters at prescribed values. The operation of the system is illustrated by maintenance of elevated axial medial stress in porcine carotid artery, while keeping the mean circumferential stress and flow-induced shear stress at baseline values. Previously unknown aspects of remodeling that might be revealed by the novel approach are discussed.

scholarly journals Morphological identification of parasitic nematode infective larvae of small ruminants and cattle: A practical lab guide

2013 ◽  
Vol 80 (1) ◽  
Author(s):  
Jan A. Van Wyk ◽  
Estelle Mayhew
Keyword(s):  
Small Ruminants ◽  
Morphological Identification ◽  
The Novel ◽  
New Approach ◽  
Novel Approach ◽  
Oesophagostomum Columbianum ◽  
Third Stage ◽  
The Common ◽  
The Mean ◽  
Distinguishing Features

In 2004, a new concept was introduced for simplifying identification of larvae of the common nematodes of cattle, sheep and goats that comprises estimates of the lengths of the sheath tail extensions of infective third-stage larvae (L3) of each genus and/or species to that of Trichostrongylus spp., instead of having to be dependent only on measurements in micrometre. For example, if the mean length of the sheath tail extension (the extension of the sheath caudad, beyond the caudal tip of the larva) of Trichostrongylus colubriformis and Trichostrongylus axei is assumed to be ‘X’, then that ofHaemonchus contortus is 2.0–2.7 ‘X’ – a difference that is not difficult to estimate. An additional new approach suggested now, particularly for L3 of species and/or genera difficult to differentiate (such as Chabertia ovina and Oesophagostomum columbianum), is to estimate the proportion of the larval sheath tail extension comprising a terminal thin, whip-like filament. For the experienced person, it is seldom necessary to measure more than one or two sheath tail extensions of L3 in a mixed culture, because the identity of most of the remaining L3 can thereafter be estimated in relation to those measured, without having to take further measurements. The aim of this article was to present the novel approach in the form of a working guide for routine use in the laboratory. To facilitate identification, figures and a separate organogram for each of small ruminants and cattle have been added to illustrate the distinguishing features of the common L3.

Exploring normative perceptions and misperceptions of private, environmentally impactful behaviours

2020 ◽  
Author(s):  
Elaine Gallagher ◽  
Bas Verplanken ◽  
Ian Walker
Keyword(s):  
Social Norms ◽  
Behaviour Change ◽  
Social Contexts ◽  
The Novel ◽  
Normative Influence ◽  
Change Mechanism ◽  
Novel Approach ◽  
Classical Studies ◽  
Referent Group

Social norms have been shown to be an effective behaviour change mechanism across diverse behaviours, demonstrated from classical studies to more recent behaviour change research. Much of this research has focused on environmentally impactful actions. Social norms are typically utilised for behaviour change in social contexts, which facilitates the important element of the behaviour being visible to the referent group. This ensures that behaviours can be learned through observation and that deviations from the acceptable behaviour can be easily sanctioned or approved by the referent group. There has been little focus on how effective social norms are in private or non-social contexts, despite a multitude of environmentally impactful behaviours occurring in the home, for example. The current study took the novel approach to explore if private behaviours are important in the context of normative influence, and if the lack of a referent groups results in inaccurate normative perceptions and misguided behaviours. Findings demonstrated variance in normative perceptions of private behaviours, and that these misperceptions may influence behaviour. These behaviours are deemed to be more environmentally harmful, and respondents are less comfortable with these behaviours being visible to others, than non-private behaviours. The research reveals the importance of focusing on private behaviours, which have been largely overlooked in the normative influence literature.

STRUKTUR NARASI NOVEL CA BAU KAN, KARYA REMY SYLADO ANALISIS SEMIOTIK

2017 ◽  
Vol 4 (1) ◽  
pp. 70
Author(s):  
Sri Sabakti
Keyword(s):  
Narrative Structure ◽  
Literary Analysis ◽  
The Novel ◽  
Basic Scheme ◽  
Library Research ◽  
The Mean

This research is aimed to expose the narrative structure of the novel Ca Bau Kan by using semiotical theory. The source of the data is the novel Ca Bau kan written by Remy Silado and published by KPG, eight edition, 2004. The data is collected by doing the library research. The teory applied in this research is the emiotical theory, especially the literary analysis of Subur Laksono Wardoyo that the analysis of the text of prose can be applied by using three fases; the analysis of the basic scheme narrative, the analysis of mean signifier, and the analysis of syntagmatics and pragmatics. The result of this research showed that the narrative structure in the novel CBK that (1) the life of Tinung before being a ca bau kan, (2) the life of Tinung as a ca bau kan, and (3) the life of Tinung after not being a ca bau kan anymore. Based on the narrative structure, it was found that “ Love is only one. No measurement is needed” is the mean signifier and able to be clarified by the analysis of syntagmatics-paradigmatics based on the biner oposition of weak x strong.AbstrakPenelitian ini bertujuan mengungkapkan stuktur narasi dalam novel Ca Bau Kan (CBK) dengan menggunakan teori semiotika. Penelitian ini menggunakan sumber data novel CBK karya Remy Silado yang diterbitkan oleh KPG, cetakan kedelapan tahun 2004. Pengumpulan data dilaksanakan dengan teknik kepustakaan. Teori yang digunakan dalam penelitian ini adalah teori semiotika, khususnya analisis sastra menurut Subur Laksono Wardoyo bahwa analisis teks prosa dapat dilakukan melalui tiga tahap, yaitu: analisis skema naratif dasar, analisis signifier utama, dan analisis sintagmatik-paradigmatik. Hasil penelitian menggambarkan bahwa struktur narasi pada novel CBK adalah sebagai berikut: 1) kehidupan Tinung sebelum menjadi ca bau kan, 2) kehidupan Tinung sebagai ca bau kan, dan 3) kehidupan Tinung setelah tidak menjadi ca bau kan. Berdasarkan struktur narasi, maka didapatkan bahwa “Cinta cuma satu, kagak perlu takaran” merupakan penanda utama dan dapat diperjelas melalui analisis sintagmatik-paradigmatik yang didasarkan atas sebuah oposisi biner lemah x kuat.

scholarly journals Multispecies for multifunctions: combining four complementary species enhances multifunctionality of sown grassland

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Matthias Suter ◽  
Olivier Huguenin-Elie ◽  
Andreas Lüscher
Keyword(s):  
Forage Quality ◽  
N Cycling ◽  
Forage Production ◽  
Mixture Effects ◽  
Novel Approach ◽  
Overall Performance ◽  
The Mean ◽  
High Forage ◽  
Diversity Effects ◽  
Species Mixtures

AbstractAssessing the overall performance of ecosystems requires a quantitative evaluation of multifunctionality. We investigated plant species diversity effects on individual functions and overall multifunctionality in a grassland experiment with sown monocultures and mixtures comprising four key grass and legume species. Nitrogen fertilisation rates were 50, 150, and 450 kg N ha−1 yr−1 (N50, N150, N450). Ten functions were measured representing forage production, N cycling, and forage quality, all being related to either productivity or environmental footprint. Multifunctionality was analysed by a novel approach using the mean log response ratio across functions. Over three experimental years, mixture effects benefited all forage production and N cycling functions, while sustaining high forage quality. Thus, mixture effects did not provoke any trade-off among the analysed functions. High N fertilisation rates generally diminished mixture benefits. Multifunctionality of four-species mixtures was considerably enhanced, and mixture overall performance was up to 1.9 (N50), 1.8 (N150), and 1.6 times (N450) higher than in averaged monocultures. Multifunctionality of four-species mixtures at N50 was at least as high as in grass monocultures at N450. Sown grass–legume mixtures combining few complementary species at low to moderate N fertilisation sustain high multifunctionality and are a ‘ready-to-use’ option for the sustainable intensification of agriculture.

scholarly journals Run-and-Tumble Motion: The Role of Reversibility

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Bart van Ginkel ◽  
Bart van Gisbergen ◽  
Frank Redig
Keyword(s):  
Free Energy ◽  
Diffusion Coefficient ◽  
Large Deviations ◽  
Energy Function ◽  
Internal State ◽  
Rate Function ◽  
Free Energy Function ◽  
Large Deviations Principle ◽  
Preferred Direction ◽  
State Process

AbstractWe study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

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