Uniform Integrability Research Articles

The Dynamics of Contagion and Behavior of the Euro Area Sovereign Bond Markets

We investigate the contagion dynamics in the main Economic and Monetary Union sovereign bond markets during the subprime and euro crises. To this end, we adopt the APARCH-ADCC model and the Markov Switching Dynamic Regression model. The impact of both crises on each country in our sample is investigated using two crisis indicators: synchronization and intensity. The empirical results show that contagious episodes and their intensities vary over time and across market pairs for both crises, thus illustrating the complexity of this phenomenon. They also reveal that the market couples composed of the Economic and Monetary Union peripheral countries were immune to the contagion of the subprime crisis and that its third phase was the most violent in terms of the intensity of the transmission of shocks. Moreover, the results show that all the countries in our sample were affected by contagion from the euro crisis, at least during one of its sub-phases. Furthermore, before the first rescue plan for the Hellenic economy, our methodology detected a contagion effect stemming from Italy, Spain, and Portugal, while intuitively one could have imagined this phenomenon coming solely from the Greek sovereign market. Finally, the analysis of the synchronization and intensity variables provides evidence of a « multi-speed Economic and Monetary Union », refuting the notion of uniform integration of the euro area sovereign bond markets. We believe that it is necessary to complete the institutional architecture of the Economic and Monetary Union to make it more resilient to shocks.

A note on the convergence of lift zonoids of measures

The lift zonoid is a convenient representation of an integrable measure by a convex set in a higher‐dimensional space. It is known that, under appropriate conditions, a uniformly integrable sequence of measures converges weakly if and only if the corresponding sequence of lift zonoids converges in the Hausdorff metric. We provide a new proof of this essential result. Our proof technique allows us to eliminate the unnecessary conditions previously considered in the literature. As a by‐product, we obtain a characterization of uniform integrability, and a simple sufficient condition for tightness, of a sequence of integrable measures in terms of their lift zonoids.

A New Version of Uniform Integrability via Power Series Summability Methods

Uniform integrability is an interesting concept in probability theory and functional analysis since it plays an important role in establishing laws of large numbers. In the literature, there are several versions of uniform integrability. Some are defined with the help of matrix summability methods, such as the Cesàro matrix, or more general methods. In this paper, we introduce a new version of uniform integrability via power series summability methods. We investigate the relationships of this new concept with some previous concepts and give $L_1$- and $L_2$-convergence results for the laws of large numbers.

Constrained Discounted Stochastic Games

In this paper, we consider a large class of constrained non-cooperative stochastic Markov games with countable state spaces and discounted cost criteria. In one-player case, i.e., constrained discounted Markov decision models, it is possible to formulate a static optimisation problem whose solution determines a stationary optimal strategy (alias control or policy) in the dynamical infinite horizon model. This solution lies in the compact convex set of all occupation measures induced by strategies, defined on the set of state–action pairs. In case of n-person discounted games the occupation measures are induced by strategies of all players. Therefore, it is difficult to generalise the approach for constrained discounted Markov decision processes directly. It is not clear how to define the domain for the best-response correspondence whose fixed point induces a stationary equilibrium in the Markov game. This domain should be the Cartesian product of compact convex sets in a locally convex topological vector space. One of our main results shows how to overcome this difficulty and define a constrained non-cooperative static game whose Nash equilibrium induces a stationary Nash equilibrium in the Markov game. This is done for games with bounded cost functions and positive initial state distribution. An extension to a class of Markov games with unbounded costs and arbitrary initial state distribution relies on an approximation of the unbounded game by bounded ones with positive initial state distributions. In the unbounded case, we assume the uniform integrability of the discounted costs with respect to all probability measures induced by strategies of the players, defined on the space of plays (histories) of the game. Our assumptions are weaker than those applied in earlier works on discounted dynamic programming or stochastic games using the so-called weighted norm approach.

Γ-convergence and stochastic homogenization of degenerate integral functionals in weighted Sobolev spaces

We study the$\Gamma$-convergence of nonconvex vectorial integral functionals whose integrands satisfy possibly degenerate growth and coercivity conditions. The latter involve suitable scale-dependent weight functions. We prove that under appropriate uniform integrability conditions on the weight functions, which shall belong to a Muckenhoupt class, the corresponding functionals$\Gamma$-converge, up to subsequences, to a degenerate integral functional defined on a limit weighted Sobolev space. The general analysis is then applied to the case of random stationary integrands and weights to prove a stochastic homogenization result for the corresponding functionals.

Lévy Processes, Generalized Moments and Uniform Integrability

Lévy Processes, Generalized Moments and Uniform Integrability

$P$-strong convergence with respect to an Orlicz function

The concepts of strong convergence, statistical convergence, and uniform integrability are of some interest in convergence theories. Recently Ünver and Orhan [19] have introduced the concepts of $P$-strong and $P$-statistical convergences with the help of power series methods and established a relationship between them. In the present paper, we introduce the notion of $P$-strong convergence with respect to an Orlicz function and prove that all these three concepts are boundedly equivalent provided that Orlicz function satisfies $\triangle _{2}-$condition. We also get an improvement of this result by using the concept of uniform integrability.

Qualitative analysis of integro-differential equations with variable retardation

<p style='text-indent:20px;'>The paper is concerned with a class of nonlinear time-varying retarded integro-differential equations (RIDEs). By the Lyapunov–Krasovski$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{ı} $ functional method, two new results with weaker conditions related to uniform stability (US), uniform asymptotic stability (UAS), integrability, boundedness, and boundedness at infinity of solutions of the RIDEs are given. For illustrative purposes, two examples are provided. The study of the results of this paper shows that the given theorems are not only applicable to time-varying linear RIDEs, but also applicable to time-varying nonlinear RIDEs.</p>

On moment convergence for some order statistics

<abstract><p>By exploring the uniform integrability of a sequence of some order statistics (OSs), we obtain the moment convergence conclusion of the sequence under some weak conditions even when the corresponding population of interest has no moment of any positive order. As an application, we embody the range of applications of a theorem presented in a reference dealing with the approximation of the difference between the moment of a sequence of normalized OSs and the corresponding moment of a standard normal distribution. By the aid of the embodied theorem, we explore the infinitesimal type of the moments of errors when we estimate some population quantiles by relative OSs. Finally, by the obtained conclusion, we can easily get a combination formula which seems hard to be proved in other methods.</p></abstract>

Differentiated Integration: The case of the European Banking Union

The European Banking Union (EBU), a system of unified financial supervision, regulation and resolution, arguably represents the biggest transfer of national sovereignty in Europe since the launch of the euro. Participation in the EBU is mandatory for the Eurozone states and voluntary for the non-Eurozone states, which makes it an example of differentiated integration (DI). This article analyses the implications of DI in the context of the EBU. The central question is whether the current EBU arrangements are going to result in uniform integration or continued differentiation. After outlining the main pillars of EBU, the article discusses whether we can envision more non-Eurozone states following the examples of Bulgaria and Croatia by opting into EBU before adoption of the euro, or whether there is a risk of more division between the EBU members and non-members. The focus is on the main economic and political considerations that affect the EBU in the medium term. The article shows that only the non-Eurozone states willing to relinquish their national sovereignty in financial supervision seek to join the EBU and that in the post-Brexit EU the differentiated EBU can potentially move towards more integration.

Correction to: On the concept of B-statistical uniform integrability of weighted sums of random variables and the law of large numbers with mean convergence in the statistical sense

Correction to: On the concept of B-statistical uniform integrability of weighted sums of random variables and the law of large numbers with mean convergence in the statistical sense

The mixed Novikov–Kazamaki type condition for the uniform integrability of the general stochastic exponential

We generalize the well known mixed Novikov–Kazamaki condition and introduce a new type sufficient condition for the uniform integrability of the stochastic exponential with jumps.

Some results concerning ideal and classical uniform integrability and mean convergence

Some results concerning ideal and classical uniform integrability and mean convergence

Double dielectric modification of nickel foam-based microwave absorbers with improved impedance matching and absorption performances

Proper physical property and well-designed microscopic structures are significant in determining the electromagnetic energy conversion. In this work, nickel foam (NiF)-based rod-like absorbers with double dielectric regulation were achieved via continuous hydrothermal reaction and subsequent heating treatment. The NiF-based uniform integration of binary metal oxides not only maintain the inherent excellent dielectric property of NiF, but also introduce extra dipolar polarizations (caused by multiple covered dielectrics) and Maxwell-Wagner-Sillars effect (induced by large dielectric property differences at the interfaces), which all contribute to the excellent microwave absorption performance. In addition, derived from the high/low dielectric synergetic effect, a balance between the introduction and dissipation of the electromagnetic energy can be realized. Based on that, the maximum bandwidth of NiF-based binary absorber reaches 7.28 GHz at 2.4 mm. This work not only provides a facile and versatile strategy to fabricate NiF-based ternary microwave absorbers, but also demonstrates the significant role of dielectric synergetic effect in optimizing microwave absorption performance.

A note on the stochastic domination condition and uniform integrability with applications to the strong law of large numbers

In this correspondence, we present new results concerning the concept of stochastic domination and apply them to obtain new results on uniform integrability and on the strong law of large numbers for sequences of pairwise independent random variables. Our result on the strong law of large numbers extends a result of Chen, Bai, and Sung (2014). The sharpness of the results is illustrated by three examples.

The uniform CLT for the empirical estimator of countable state space semi-Markov kernels indexed by functions with applications

This paper is concerned with the uniform CLT for an empirical estimator of countable state space semi-Markov processes indexed by functions under the uniformly integrable entropy condition. The results of this paper generalise those of Limnios [(2004), ‘A Functional Central Limit Theorem for the Empirical Estimator of a Semi-Markov Kernel’, Journal of Nonparametric Statistics, 16(1–2), 13–18. The International Conference on Recent Trends and Directions in Nonparametric Statistics]. We apply our results to the following important topics: on the kernel-type estimator of the semi-Markov kernel, the weak convergence of the smoothed empirical semi-Markov processes, we introduce the copula estimators in the semi-Markov framework and we establish their limiting laws by using the functional delta methods. We prove the main results for the uniform CLT via a martingale difference sequence as in Bae et al. [(2010), ‘The Uniform CLT for Martingale Difference Arrays Under the Uniformly Integrable Entropy’, Bulletin of the Korean Mathematical Society, 47(1), 39–51].

One-step preparation of tubular nanofibers and micro/nanospheres covered membrane with 3D micro/nano structure for highly efficient emulsified oil/water separation

Facile fabrication of superwetting materials is urgently desired, which remains a challenging issue for industrial oily wastewater treatment. In this study, a novel tubular nanofibers and micro/nanospheres covered PVDF/graphene (GE) composite membrane (TPGCM) was prepared via one-step simultaneous electrospinning/electrospraying process with the polyethylene terephthalate (PET) braided tube (BrT) as the support. This simple combined technique allowed the uniform integration of PVDF micro/nanospheres and GE nanosheets into the PVDF nanofibrous network to form a 3D hierarchical micro/nano structural composite membrane. The resultant membrane exhibited superoleophilicity in air with oil contact angle of 0°, and showed under oil superhydrophobicity with corresponding contact angle of 159 ± 0.8°. Furthermore, the morphology of the covered micro/nanospheres was simply controlled by adjusting GE nanosheets content in electrospraying precursor. As-prepared TPGCM can effectively separate a series of Span-80-stabilized water-in-oil emulsions, which showed outstanding separation efficiency of up to 99.8 %. Moreover, the robust recyclability was also presented with separation efficiency of more than 99.3 % after 10 cycles. Our strategy possesses the advantages of simplicity and cost saving, avoiding complicated reaction or post treatment, thus indicating its scalable application for practical oily wastewater purification.

Identification of Degrading Effects in the Operation of Neighboring Photovoltaic Systems in Urban Environments

As photovoltaics technologies have emerged as one of the most promising renewable energy resources in urban environments, monitoring and maintaining of such systems have gained significance. In order to support reliable system operation during the projected in-field operation lifetime, effective strategies for identifying potential problems in photovoltaic systems operation are needed. In this paper, novel methods for the identification of degrading effects in the operation of neighboring photovoltaic systems are presented. The proposed methods are applicable for identifying panel aging properties, soiling effects, and the operation of photovoltaic systems under different shading scenarios. Since the proposed methods are based on the cross-correlation of the operation of neighboring systems, they are particularly suitable performance assessment in urban environments. The proposed identification methods are integrated according to the adopted fog computing model, providing a scalable solution capable of uniform integration into the distributed applications for monitoring and maintenance of photovoltaic systems in urban areas. The details regarding the implementation of the identification methods in the form of data processing services and service operation and dependencies are also provided in this paper. The identification methods, integration concept, and related service operation are verified through the presented case study.

Multivariate goodness-of-fit tests based on Wasserstein distance

Goodness-of-fit tests based on the empirical Wasserstein distance are proposed for simple and composite null hypotheses involving general multivariate distributions. For group families, the procedure is to be implemented after preliminary reduction of the data via invariance. This property allows for calculation of exact critical values and p-values at finite sample sizes. Applications include testing for location–scale families and testing for families arising from affine transformations, such as elliptical distributions with given standard radial density and unspecified location vector and scatter matrix. A novel test for multivariate normality with unspecified mean vector and covariance matrix arises as a special case. For more general parametric families, we propose a parametric bootstrap procedure to calculate critical values. The lack of asymptotic distribution theory for the empirical Wasserstein distance means that the validity of the parametric bootstrap under the null hypothesis remains a conjecture. Nevertheless, we show that the test is consistent against fixed alternatives. To this end, we prove a uniform law of large numbers for the empirical distribution in Wasserstein distance, where the uniformity is over any class of underlying distributions satisfying a uniform integrability condition but no additional moment assumptions. The calculation of test statistics boils down to solving the well-studied semi-discrete optimal transport problem. Extensive numerical experiments demonstrate the practical feasibility and the excellent performance of the proposed tests for the Wasserstein distance of order p=1 and p=2 and for dimensions at least up to d=5. The simulations also lend support to the conjecture of the asymptotic validity of the parametric bootstrap.

Условие равномерной интегрируемости экспоненциальных мартингалов

В статье доказано новое достаточное условие для равномерной интегрируемости экспоненциальных локальных мартингалов. Условие сформулировано в терминах квадратической вариации локального мартингала. Оно обобщает ряд известных достаточных условий подобного рода. In the article it is suggested a new sufficient condition for uniform integrability of continues exponential local martingales. It is shown that the condition is much weaker then a number of known sufficient conditions for uniform integrability of exponential local martingales.