General N-th Degree Stochastic Dominance

This paper examines N-th degree stochastic dominance which is used to compare the risk factor of risky assets after summarizing the definitions of first degree stochastic dominance and second degree stochastic dominance. The paper defines general N-th degree stochastic dominance, presents a sufficient and necessary condition which is the equivalent theorem of general N-th degree stochastic dominance. The feasible utility form is constructed to explain the economic meaning of N-th degree stochastic dominance in the field of financial economics. The equivalent condition is described by the probability distribution functions of risky assets, which are not related to utility functions (preference relations).

CONVEX CONCENTRATION INEQUALITIES FOR CONTINUOUS GAS AND STOCHASTIC DOMINATION

In this article, we consider the continuous gas in a bounded domain ∧ of R^＋ or R^d described by a Gibbsian probability measure μη∧ associated with a pair interaction φ, the inverse temperature β, the activity z 〉 0, and the boundary condition η. Define F ∫ωf（s）wA（ds）. Applying the generalized Ito＇s formula for forward-backward martingales （see Klein et M. [5]）, we obtain convex concentration inequalities for F with respect to the Gibbs measure μη∧. On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure.

Analyzing multidimensional measures of poverty and their influences in China's Qinba Mountains

We use the Alkire–Foster poverty measure and decomposition method to study multidimensional poverty in the Qinling–Daba contiguous poor area of China's Henan Province.We examine absolute,relative,and multidimensional poverty focusing on heads of household and family characteristics as constituents of escaping each.We find that the multidimensional poverty index declines to a low level as values of k increase.Combining first-order random dominance with second-order stochastic dominance quickly determines rankings in the multidimensional poverty index.Increasing non-agricultural income emerges as the most important influence on escaping rural poverty,whereas households with elderly and children are at greatest risk for falling into poverty.

On the strong convergence properties for weighted sums of negatively orthant dependent random variables

In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.

Discovering admissible Web services with uncertain QoS

Open and dynamic environments lead to inher- ent uncertainty of Web service QoS （Quality of Service）, and the QoS-aware service selection problem can be looked upon as a decision problem under uncertainty. We use an empiri- cal distribution function to describe the uncertainty of scores obtained from historical transactions. We then propose an approach to discovering the admissible set of services in- cluding alternative services that are not dominated by any other alternatives according to the expected utility criterion. Stochastic dominance （SD） rules are used to compare two services with uncertain scores regardless of the distribution form of their uncertain scores. By using the properties of SD rules, an algorithm is developed to reduce the number of SD tests, by which the admissible services can be reported pro- gressively. We prove that the proposed algorithm can be run on partitioned or incremental alternative services. Moreover, we achieve some useful theoretical conclusions for correct pruning of unnecessary calculations and comparisons in each SD test, by which the efficiency of the SD tests can be im- proved. We make a comprehensive experimental study using real datasets to evaluate the effectiveness, efficiency, and scal- ability of the proposed algorithm.