A Rigorous Proof of Fundamental Theorem of Uncertain Calculus

2021 ◽  
pp. 2150009
Author(s):  
Tingqing Ye
Keyword(s):  
Fundamental Theorem ◽  
Rigorous Proof ◽  
Lipschitz Continuous ◽  
Sample Paths ◽  
Liu Process ◽  
Locally Lipschitz ◽  
Definition Of ◽  
Almost All ◽  
Uncertain Calculus ◽  
And Diffusion

This paper revises the definition of the general Liu process via requiring its drift and diffusion to be sample-continuous. Then it is verified that almost all sample paths of the general Liu process are locally Lipschitz continuous. At last, a rigorous proof of fundamental theorem of uncertain calculus is given.

Limit measures and ergodicity of fractional stochastic reaction–diffusion equations on unbounded domains

2021 ◽  
pp. 2140012
Author(s):  
Zhang Chen ◽  
Bixiang Wang
Keyword(s):  
Invariant Measures ◽  
Unbounded Domains ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Lipschitz Continuous ◽  
Bounded Interval ◽  
Locally Lipschitz ◽  
Stochastic Reaction ◽  
And Diffusion

This paper deals with invariant measures of fractional stochastic reaction–diffusion equations on unbounded domains with locally Lipschitz continuous drift and diffusion terms. We first prove the existence and regularity of invariant measures, and then show the tightness of the set of all invariant measures of the equation when the noise intensity varies in a bounded interval. We also prove that every limit of invariant measures of the perturbed systems is an invariant measure of the corresponding limiting system. Under further conditions, we establish the ergodicity and the exponentially mixing property of invariant measures.

scholarly journals On regularization by a small noise of multidimensional ODEs with non-Lipschitz coefficients

2020 ◽  
Vol 72 (9) ◽  
pp. 1254-1285
Author(s):  
A. Pilipenko ◽  
A. Kulik
Keyword(s):  
Selection Problem ◽  
Extremal Solutions ◽  
Averaging Principle ◽  
Small Noise ◽  
Lipschitz Continuous ◽  
Limit Process ◽  
Locally Lipschitz ◽  
And Diffusion ◽  
Locally Lipschitz Continuous

UDC 519.21 In this paper we solve a selection problem for multidimensional SDE where the drift and diffusion are locally Lipschitz continuous outside of a fixed hyperplane It is assumed that the drift has a Hoelder asymptotics as approaches and the limit ODE does not have a unique solution.We show that if the drift pushes the solution away from then the limit process with certain probabilities selects some extremal solutions to the limit ODE. If the drift attracts the solution to then the limit process satisfies an ODE with some averaged coefficients. To prove the last result we formulate an averaging principle, which is quite general and new.

scholarly journals No Infimum Gap and Normality in Optimal Impulsive Control Under State Constraints

2021 ◽  
Author(s):  
Giovanni Fusco ◽  
Monica Motta
Keyword(s):  
Original Problem ◽  
State Constraints ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Continuous Data ◽  
Lipschitz Continuous ◽  
Extended Sense ◽  
Unbounded Controls ◽  
Locally Lipschitz ◽  
Optimal Impulsive Control

AbstractIn this paper we consider an impulsive extension of an optimal control problem with unbounded controls, subject to endpoint and state constraints. We show that the existence of an extended-sense minimizer that is a normal extremal for a constrained Maximum Principle ensures that there is no gap between the infima of the original problem and of its extension. Furthermore, we translate such relation into verifiable sufficient conditions for normality in the form of constraint and endpoint qualifications. Links between existence of an infimum gap and normality in impulsive control have previously been explored for problems without state constraints. This paper establishes such links in the presence of state constraints and of an additional ordinary control, for locally Lipschitz continuous data.

On the Role of Charged Defect States and Deep Traps in the Photocarrier Drift and Diffusion in a-Si:H

2000 ◽  
Vol 609 ◽  
Author(s):  
Paul Stradins ◽  
Akihisa Matsuda
Keyword(s):  
Particle Number ◽  
Defect States ◽  
Total Electron ◽  
Minority Carrier Diffusion Length ◽  
Continuity Equations ◽  
Effective Mobility ◽  
Almost All ◽  
Charged Defects ◽  
And Diffusion

ABSTRACTThe drift and diffusion in the presence of charged defects and photocarriers trapped in the tail states is re-examined. In continuity equations, diffusive and drift currents are related to free particles while the Poisson equation includes all charges. In order to make use of ambipolar diffusion approximation, the mobilities and diffusion coefficients should be attributed to the total electron and hole populations making them strongly particle-number dependent. Due to the asymmetry of the conduction and valence band tails, almost all trapped electrons reside in negatively charged defects (D−). A simple model of photocarrier traffic via tail and defect states allows to establish the effective mobility values and coefficients in Einstein relations. In a photocarrier grating experiment, grating of D− is counterbalanced by the grating of trapped holes. Nevertheless, electrons remain majority carriers, allowing the measurement of minority carrier diffusion length, but analysis is needed to relate the latter with μτ product.

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.

Pricing Convertible Bond in Uncertain Financial Market

2021 ◽  
pp. 2150007
Author(s):  
Zhiqiang Zhang ◽  
Zhenfang Wang ◽  
Xiaowei Chen
Keyword(s):  
Differential Equation ◽  
Financial Market ◽  
Stock Price ◽  
Uncertainty Theory ◽  
Convertible Bonds ◽  
Convertible Bond ◽  
Uncertain Differential Equation ◽  
Numerical Examples ◽  
Liu Process ◽  
Uncertain Calculus

This paper is devoted to evaluating the convertible bonds within the framework of uncertainty theory. Under the assumption that the underlying stock price follows an uncertain differential equation driven by Liu process, the price formulas of convertible bonds and the callable convertible bonds are derived by using the method of uncertain calculus. Finally, two numerical examples are discussed.

scholarly journals Legal status of cryptocurrency in Asian countries

2021 ◽  
Vol 66 ◽  
pp. 96-102
Author(s):  
V.M. Logoida
Keyword(s):  
Civil Rights ◽  
Government Regulation ◽  
Legal Status ◽  
Legal Regulation ◽  
Intangible Asset ◽  
Asian Countries ◽  
Legal Nature ◽  
Liberal Approach ◽  
Definition Of ◽  
Almost All

The article is devoted to the study of the experience of legal regulation of the legal status of cryptocurrencies and transactions with them in Asian countries (except for the People's Republic of China and Asian countries - members of the Commonwealth of Independent States, as the author examined them in separate publications). In the article the author, based on the study of regulations, administrative and judicial practice of all major countries in this part of the world, emphasizes the divergent trends in cryptocurrency transactions regulation in the region, when some countries move from a liberal approach to the use of cryptocurrencies to their total ban and vice versa. It is noted that almost all countries in the region give a legal assessment of the payment function of cryptocurrencies, using regulatory or prohibitive approaches, depending on the chosen policy, which indirectly confirms their understanding of the legal nature of cryptocurrencies primarily as a means of payment. At the same time, these countries not only categorically distinguish cryptocurrencies from fiat money issued by central banks, but also mostly avoid the official definition of cryptocurrency as private (decentralized) cash, preferring to qualify them as an intangible asset, virtual asset, digital asset, financial value and even a good or service, which is currently a kind of compromise between political expediency and economic realities. The author also notes that the Asian region is characterized by very active attempts to resolve the legal status of cryptocurrencies at the legislative level, and not just administrative or judicial response to the actual legal relationship, although the progress of different countries in this matter is different. As a result, the author concludes that in the Asian countries considered in the article, there is no same view on the legal nature of cryptocurrency, its qualification as an object of civil rights, and ways to regulate transactions with it (libertarian approach, positive-cryptocurrency approach but with detailed government regulation and control or a completely restrictive policy in relation to the cryptocurrency market).

scholarly journals The Tax Cuts and Jobs Act and the Middle Class

2019 ◽  
Vol 26 (01) ◽  
pp. 53
Author(s):  
Deborah Combs ◽  
Brian Nichols
Keyword(s):  
Middle Class ◽  
The United States ◽  
Census Bureau ◽  
Tax Rates ◽  
United States Census ◽  
United States Census Bureau ◽  
Definition Of ◽  
Almost All ◽  
Jobs Act ◽  
Tax Cuts

This paper explores how the tax cuts and jobs act of 2017 impacts middle-class taxpayers by calculating the tax liability at different levels of income and deductions in 2017 versus 2018. The results confirm the statements supporting the positive effect of the tax change for the middle class. The tax cut and jobs act eliminates personal exemptions, changes the standard deductions at various incomes and family sizes, and lowers marginal tax rates. After providing details of the act, this research examines the definition of the U.S. middle class by using prior research from the Pew Research Center, the United States Census Bureau, and the federal reserve to determine which income levels are attributable to the middle class. Then the tax liability for these income classes is calculated for single and married filing jointly taxpayers in both 2017 and 2018 to determine if the tax cuts and jobs act reduces the tax liability for the middle class. The results show that in almost all scenarios the tax liability in 2018 will be lower than in 2017, regardless of whether standard or itemized deductions are taken. The marriage penalty is no longer applicable, and the new tax act provides a substantial benefit to large families

Historical Account or Discourse on Identity? A Reexamination of Fulbe Hegemony and Autochthonous Submission in Banyo

1998 ◽  
Vol 25 ◽  
pp. 93-110 ◽  
Author(s):  
Quentin Gausset
Keyword(s):  
Nineteenth Century ◽  
The Other ◽  
Islamic State ◽  
Local Populations ◽  
Northern Cameroon ◽  
Definition Of ◽  
Historical Accounts ◽  
In The Beginning ◽  
Almost All ◽  
The Military

Traditional accounts of the nineteenth-century Fulbe conquest in northern Cameroon tell roughly the same story: following the example of Usman Dan Fodio in Nigeria, the Fulbe of Cameroon organized in the beginning of the nineteenth century a “jihad” or a “holy war” against the local pagan populations to convert them to Islam and create an Islamic state. The divisions among the local populations and the military superiority of the Fulbe allowed them to conquer almost all northern Cameroon. They forced those who submitted to give an annual tribute of goods and servants, and they raided the other groups. In these traditional accounts the Fulbe are presented as unchallenged masters, while the local populations are depicted as slaves who were powerless over their fate; their role in the conquest of the region and in the administration of the new political order is supposed to have been insignificant.I will show that, on the contrary, in the area of Banyo the Wawa and Bute played a crucial role in the conquest of the sultanate and in its administration. I will then re-examine the cliche that all members of the local populations were the slaves of the Fulbe by distinguishing the fate of the Wawa and Bute on one side from that of the Kwanja and Mambila on the other, and by showing the importance of the Fulbe's identity in shaping the definition of slavery. Finally I will argue that, if the historical accounts found in the scientific literature invariably insist on Fulbe hegemony and minimize the role played by the local populations, it is because those accounts are often based on Fulbe traditions, and because these traditions are remodeled by the Fulbe in order to correspond to their discourse on identity.

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