We theoretically compare variances between the Infinitesimal Perturbation Analysis (IPA) estimator and the Likelihood Ratio (LR) estimator to Monte Carlo gradient for stochastic systems. The conditions proposed in [Cui et al., 2020] when the IPA estimator has a smaller variance can yield sharper...

Two notions of fractional stochastic dominance are recently proposed by Muller et al. (2017) and Huang et al. (2020), respectively. Our main objective is to understand the comparative advantages of the two notions, as well as their suitability in different contexts, by establishing several new...

This paper investigates whether and when fractional degree stochastic dominance rules can inherit the invariance properties of integer-degree stochastic dominance. Within a general formulation, we first show that it is impossible for fractional degree stochastic dominance to obey all the six...