Two-person zero-sum stochastic games are considered under the long-run average expected payo ̈ criterion. State and action spaces are assumed ®nite. By making use of the concept of maximal communicating classes, the following decomposition algorithm is introduced for solving twoperson zero-sum stochastic games: First, the state space is decomposed into maximal communicating classes. Then, these ...

In this work, we review the stochastic decomposition for the number of customers in M/G/1 retrial queues with reliable server and server subjected to breakdowns which has been the subject of investigation in the literature. Using the decomposition property of M/G/1 retrial queues with breakdowns that holds under exponential assumption for retrial times as an approximation in the non-exponential...

We propose a novel distributed method for convex optimization problems with a certain separability structure. The method is based on the augmented Lagrangian framework. We analyze its convergence and provide an application to two network models, as well as to a two-stage stochastic optimization problem. The proposed method compares favorably to two augmented Lagrangian decomposition methods kno...

This paper reconciles two widely used decompositions of GDP into trend and cycle that yield starkly different results. The BeveridgeNelson (BN) decomposition implies that a stochastic trend accounts for most of the variation in output, whereas the unobserved-components (UC) implies cyclical variation is dominant. Which is correct has broad implications for the relative importance of real versus...

The decomposition of a sample of images on a relevant subspace is a recurrent problem in many different fields from Computer Vision to medical image analysis. We propose in this paper a new learning principle and implementation of the generative decomposition model generally known as noisy ICA (for independent component analysis) based on the SAEM algorithm, which is a versatile stochastic appr...

The series representation consisting of eigenfunctions as the orthogonal basis is called the Karhunen–Loeve expansion. This paper demonstrates that the determination of eigensolutions using a wavelet-Galerkin scheme for Karhunen–Loeve expansion is computationally equivalent to using wavelet directly for stochastic expansion and simulating the correlated random coefficients using eigen decomposi...

We consider decomposition approaches for the solution of multistage stochastic programs that appear in financial applications. In particular, we discuss the performance of two algorithms that we test on the mean-variance portfolio optimization problem. The first algorithm is based on a regularized version of Benders decomposition, and we discuss its extension to the quadratic case. The second a...

0. Systems theory I. Part 1: Convergence A. Two approaches to convergence B. A mathematical formulation of convergence C. Convergence is a Markov process D. Starting configuration doesn’t matter II. Part 2: Analysis A. Background and mathematical foundation 1. Stochastic matrices 2. The Eigenvalue problem 3. Spectral Decomposition 4. Spectral Decomposition of M B. The Algebraic View 1. Partitio...

Based on the polyhedral representation of Künzi-Bay and Mayer (2006), we propose decomposition frameworks for handling CVaR objectives and constraints in two-stage stochastic models. For the solution of the decomposed problems we propose special Level-type methods.

We give a brief introduction to the class of stochastic processes known as Lévy processes, concentrating principally on their relation with infinitely divisible distributions and the Lévy-Itô decomposition.