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Computational schemes for two exponential servers where the first has a finite buffer

Moshe Haviv, Rita Zlotnikov (2011)

RAIRO - Operations Research

We consider a system consisting of two not necessarily identical exponential servers having a common Poisson arrival process. Upon arrival, customers inspect the first queue and join it if it is shorter than some threshold n. Otherwise, they join the second queue. This model was dealt with, among others, by Altman et al. [Stochastic Models20 (2004) 149–172]. We first derive an explicit expression for the Laplace-Stieltjes transform of the distribution underlying the arrival (renewal) process to...

Computing the Stackelberg/Nash equilibria using the extraproximal method: Convergence analysis and implementation details for Markov chains games

Kristal K. Trejo, Julio B. Clempner, Alexander S. Poznyak (2015)

International Journal of Applied Mathematics and Computer Science

In this paper we present the extraproximal method for computing the Stackelberg/Nash equilibria in a class of ergodic controlled finite Markov chains games. We exemplify the original game formulation in terms of coupled nonlinear programming problems implementing the Lagrange principle. In addition, Tikhonov's regularization method is employed to ensure the convergence of the cost-functions to a Stackelberg/Nash equilibrium point. Then, we transform the problem into a system of equations in the...

Condiciones de martingala sobre un proceso de aprendizaje tipo beta con dos operadores y reforzamiento no contingente simple. 2. Caso general.

Juan Ignacio Domínguez Martínez (1985)

Trabajos de Estadística e Investigación Operativa

Se analizan las condiciones bajo las cuales un modelo de aprendizaje no lineal (modelo beta) con dos operadores y reforzamiento no contingente simple es una sub(super)martingala en el supuesto de que todas las respuestas sean reforzadas, generalizándose al caso de ausencia de reforzamiento.Las condiciones establecidas, que nos conducen a 23 casos posibles, permiten analizar exhaustivamente el comportamiento asintótico del modelo y compararlo con la clasificación de Norman.

Conditional distributions, exchangeable particle systems, and stochastic partial differential equations

Dan Crisan, Thomas G. Kurtz, Yoonjung Lee (2014)

Annales de l'I.H.P. Probabilités et statistiques

Stochastic partial differential equations (SPDEs) whose solutions are probability-measure-valued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particular, we consider a model of asset price determination by an infinite collection of competing traders. Each trader’s valuations of the assets are given by the solution of a stochastic differential equation,...

Conditional limit theorems for intermediately subcritical branching processes in random environment

V. I. Afanasyev, Ch. Böinghoff, G. Kersting, V. A. Vatutin (2014)

Annales de l'I.H.P. Probabilités et statistiques

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition appears. In this paper we study the intermediately subcritical case, which constitutes the borderline within this phase transition. We study the asymptotic behavior of the survival probability. Next the size of the population and the shape of the random environment...

Conditional Markov chains - construction and properties

Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Niewęgłowski (2015)

Banach Center Publications

In this paper we study finite state conditional Markov chains (CMCs). We give two examples of CMCs, one which admits intensity, and another one, which does not admit an intensity. We also give a sufficient condition under which a doubly stochastic Markov chain is a CMC. In addition we provide a method for construction of conditional Markov chains via change of measure.

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