Stochastic Precedence and Minima Among Dependent Variables

Wavelets for Nonparametric Stochastic Regression with Pairwise Negative Quadrant Dependent Random Variables

We propose a wavelet based stochastic regression function estimator for the estimation of the regression function for a sequence of pairwise negative quadrant dependent random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator are investigated. It is found that the estimators have similar properties to their counterparts st...

Weighted Means in Stochastic Approximation of Minima∗

Weighted averages of Kiefer–Wolfowitz-type procedures, which are driven by larger step lengths than usual, can achieve the optimal rate of convergence. A priori knowledge of a lower bound on the smallest eigenvalue of the Hessian matrix is avoided. The asymptotic mean squared error of the weighted averaging algorithm is the same as would emerge using a Newton-type adaptive algorithm. Several di...

Stochastic Machine Scheduling with Precedence Constraints

We consider parallel, identical machine scheduling problems where the jobs are subject to precedence constraints, release dates, and the processing times of jobs are governed by independent probability distributions. The objective is to minimize the expected value of the total weighted completion time ∑w j C j , where w j 0. Building upon a linear programming relaxation by Möhring, Schulz, and ...

Stochastic Online Scheduling with Precedence Constraints

We consider the preemptive and non-preemptive problems of scheduling jobs with precedence constraints on parallel machines with the objective to minimize the sum of (weighted) completion times. We investigate an online model in which the scheduler learns about a job when all its predecessors have completed. For scheduling on a single machine, we show matching lower and upper bounds of Θ(n) and ...

Central and Local Limit Theories in Markov Dependent Random Variables