A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and other one expected utilities. In early days, Fishburn investigated SD we refer this perspective as Fishburn’s SD. his many results was development fractional-order for continuous distributions. However, discrete cannot directly generalized, because some properties fractiona...

‎In the present paper‎, ‎optimal heating of temperature field which is modelled as a boundary optimal control problem‎, ‎is investigated in the uncertain environments and then it is solved numerically‎. ‎In physical modelling‎, ‎a partial differential equation with stochastic input and stochastic parameter are applied as the constraint of the optimal control problem‎. ‎Controls are implemented ...

Abstract We consider a second‐order linear system of ordinary differential equations (ODEs) including random variables. A stochastic Galerkin method yields larger deterministic ODEs. apply model order reduction (MOR) this high‐dimensional dynamical system, where its internal energy represents quadratic quantity interest. investigate the properties MOR with respect to stability, passivity and di...

 In this paper, we study stochastic comparisons of order statistics of independent random variables with proportional hazard rates, using the notion of variance majorization.

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method pos...