scholarly journals On the Upper and Lower Class For Gaussian Processes with Several Parameters

1969 ◽  
Vol 35 ◽  
pp. 109-132 ◽  
Author(s):  
Takayuki Kawada
Keyword(s):  
Brownian Motion ◽  
Gaussian Processes ◽  
Hölder Continuity ◽  
Integral Form ◽  
Lower Class ◽  
Uniform Continuity ◽  
Upper Class ◽  
Holder Continuity ◽  
Definition Of ◽  
Almost All

1.In the study on Hölder-continuity of Brownian motion, A.N.Kol-mogorov introduced the concept of upper and lower classes and presented a criterion with the integral form to test whether some function belongs to upper or lower class; the so-called Kolmogorov’s test (I.Petrovesky [10]). P.Lévy considered the upper and lower class with regard to the uniform continuity of Brownian motion. We shall recall the definition of the upper and lower classes. We shall call <p(t) a function belonging to the upper class with regard to the uniform continuity of Brownian motion x(t) if there exists a positive number s{w) such that, for almost all w,implies(1.1)

scholarly journals Fractionally integrated Bessel process

2021 ◽  
Vol 477 (2250) ◽  
pp. 20200934
Author(s):  
Georgiy Shevchenko ◽  
Dmytro Zatula
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Hölder Continuity ◽  
Bessel Process ◽  
Holder Continuity ◽  
Basic Properties

We consider a fractionally integrated Bessel process defined by Y s δ , H = ∫ 0 ∞ ( u H − ( 1 / 2 ) − ( u − s ) + H − ( 1 / 2 ) ) d X u δ , where X δ is the Bessel process of dimension δ  > 2. We discuss the relation of this process to the fractional Brownian motion at its maximum, study the basic properties of the process and prove its Hölder continuity.

scholarly journals Brazil’s Innovative Anti-Poverty & Inequality Model

2014 ◽  
Vol 1 (2) ◽  
pp. 56-61 ◽  
Author(s):  
Abdul Ghafoor Awan
Keyword(s):  
Income Inequality ◽  
Secondary Data ◽  
Lower Class ◽  
Upper Class ◽  
Tax Rates ◽  
Brazilian Government ◽  
General Terms ◽  
Poverty And Inequality ◽  
Almost All ◽  
Different Characteristics

Introduction: Poverty and income inequality were two main problems of Brazil. In order to solve these problems Brazil has taken different policy initiatives. The economists call it an innovative anti-poverty and inequality model. Objectives: The objectives of this paper are to study different aspects of Brazilian innovative anti-poverty and inequality model and its impact on Brazilian society. Another objective to study is whether this model is specification in its applicability or it may be applied on other medium-income economies because income inequality and poverty are the common problems of almost all developing countries. Methodology of study: This is a qualitative research study in which we have studied different characteristics in general terms and policies introduced by the Brazilian government during 2000-2010 periods. We have used secondary data extracted from the database of IMF, World Bank, US Federal Reserves, US Bureau of Economic Analysis and relevant journals. Results & conclusions: Our study finds hat poverty in Brazil has reduced from 17 percent in 2000 to 8 percent in 2010. The evidence also shows that the wealth of the richest 20 percent of upper class was decreased during 2000-2010 due to high tax rates payment and the income of lowest 20 percent quintile was increased from 2.6 percent to 3.5 percent in the same period. It shows that the income of lower class was increased while the wealth and income of upper class was decreased during 2000-2010. The study also reveals that about half of the poor segment of Brazilian population has come out of the poverty trap in a short span of just 10 years.

On nonhomeomorphic mappings with the inverse Poletsky inequality

2020 ◽  
Vol 17 (3) ◽  
pp. 414-436
Author(s):  
Evgeny Sevost'yanov ◽  
Serhii Skvortsov ◽  
Oleksandr Dovhopiatyi
Keyword(s):  
Boundary Behavior ◽  
Hölder Continuity ◽  
Continuous Extension ◽  
Quasiconformal Mappings ◽  
Holder Continuity ◽  
Hölder Continuous ◽  
Finite Distortion ◽  
Mappings Of Finite Distortion ◽  
Lipschitz Continuous ◽  
Inverse Inequality

As known, the modulus method is one of the most powerful research tools in the theory of mappings. Distortion of modulus has an important role in the study of conformal and quasiconformal mappings, mappings with bounded and finite distortion, mappings with finite length distortion, etc. In particular, an important fact is the lower distortion of the modulus under mappings. Such relations are called inverse Poletsky inequalities and are one of the main objects of our study. The use of these inequalities is fully justified by the fact that the inverse inequality of Poletsky is a direct (upper) inequality for the inverse mappings, if there exist. If the mapping has a bounded distortion, then the corresponding majorant in inverse Poletsky inequality is equal to the product of the maximum multiplicity of the mapping on its dilatation. For more general classes of mappings, a similar majorant is equal to the sum of the values of outer dilatations over all preimages of the fixed point. It the class of quasiconformal mappings there is no significance between the inverse and direct inequalities of Poletsky, since the upper distortion of the modulus implies the corresponding below distortion and vice versa. The situation significantly changes for mappings with unbounded characteristics, for which the corresponding fact does not hold. The most important case investigated in this paper refers to the situation when the mappings have an unbounded dilatation. The article investigates the local and boundary behavior of mappings with branching that satisfy the inverse inequality of Poletsky with some integrable majorant. It is proved that mappings of this type are logarithmically Holder continuous at each inner point of the domain. Note that the Holder continuity is slightly weaker than the classical Holder continuity, which holds for quasiconformal mappings. Simple examples show that mappings of finite distortion are not Lipschitz continuous even under bounded dilatation. Another subject of research of the article is boundary behavior of mappings. In particular, a continuous extension of the mappings with the inverse Poletsky inequality is obtained. In addition, we obtained the conditions under which the families of these mappings are equicontinuous inside and at the boundary of the domain. Several cases are considered: when the preimage of a fixed continuum under mappings is separated from the boundary, and when the mappings satisfy normalization conditions. The text contains a significant number of examples that demonstrate the novelty and content of the results. In particular, examples of mappings with branching that satisfy the inverse Poletsky inequality, have unbounded characteristics, and for which the statements of the basic theorems are satisfied, are given.

scholarly journals Linearization and Hölder continuity for nonautonomous systems

2021 ◽  
Vol 297 ◽  
pp. 536-574
Author(s):  
Lucas Backes ◽  
Davor Dragičević ◽  
Kenneth J. Palmer
Keyword(s):  
Hölder Continuity ◽  
Holder Continuity ◽  
Nonautonomous Systems

scholarly journals Frege’s puzzle and the ex ante Pareto principle

2020 ◽  
Author(s):  
Anna Mahtani
Keyword(s):  
Policy Choice ◽  
Choice Situation ◽  
Pareto Principle ◽  
Social Situations ◽  
Central Importance ◽  
Ex Ante ◽  
Definition Of ◽  
Almost All ◽  
Rational Behaviour ◽  
Fixed Population

Abstract The ex ante Pareto principle has an intuitive pull, and it has been a principle of central importance since Harsanyi’s defence of utilitarianism (to be found in e.g. Harsanyi, Rational behaviour and bargaining equilibrium in games and social situations. CUP, Cambridge, 1977). The principle has been used to criticize and refine a range of positions in welfare economics, including egalitarianism and prioritarianism. But this principle faces a serious problem. I have argued elsewhere (Mahtani, J Philos 114(6):303-323 2017) that the concept of ex ante Pareto superiority is not well defined, because its application in a choice situation concerning a fixed population can depend on how the members of that population are designated. I show in this paper that in almost all cases of policy choice, there will be numerous sets of rival designators for the same fixed population. I explore two ways that we might complete the definition of ex ante Pareto superiority. I call these the ‘supervaluationist’ reading and the ‘subvaluationist’ reading. I reject the subvaluationist reading as uncharitable, and argue that the supervaluationist reading is the most promising interpretation of the ex ante Pareto principle. I end by exploring some of the implications of this principle for prioritarianism and egalitarianism.

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