In this paper we present a stability analysis of a stochastic optimization problem with
stochastic second order dominance constraints. We consider a perturbation of the …

Abstract Conditional Value at Risk (CVaR) has been recently used to approximate a chance
constraint. In this paper, we study the convergence of stationary points, when sample …

A Vitali convergence theorem is proved for subspaces of an abstract convex combination
space which admits a complete separable metric. The convergence may be in that metric or …

Sample average approximation (SAA) method has recently been applied to solve stochastic
programs with second order stochastic dominance (SSD) constraints. In particular, Hu et …

Jensen's inequality is extended to metric spaces endowed with a convex combination
operation. Applications include a dominated convergence theorem for both random …

Shapiro and Xu (2008)[17] investigated uniform large deviation of a class of Hölder
continuous random functions. It is shown under some standard moment conditions that with …

Recently, Balaji and Xu studied the consistency of stationary points, in the sense of the
Clarke generalized gradient, for the sample average approximations to a one-stage …

Consider the Strong Law of Large Numbers for t-normed averages of fuzzy random
variables in the uniform metric d∞. That probabilistic property is known to hold when the t …

In the paper we establish a strong graphical law of large numbers (LLN) for random outer
semicontinuous mappings, providing conditions when graphs of sample average mappings …

The study of random geometrical objects goes back to the famous Buffon needle problem.
Similar to the ideas of Geometric Probability, which can be traced back to the very origins of …