Ergodicity, Stabilization, and Singular Perturbations for Bellman-Isaacs Equations (Memoirs of the American Mathematical Society Series)

Ergodicity, Stabilization, and Singular Perturbations for Bellman-Isaacs Equations (Memoirs of the American Mathematical Society Series)

by Olivier Alvarez, Martino Bardi
     
 

ISBN-10: 0821847155

ISBN-13: 9780821847152

Pub. Date: 02/22/2010

Publisher: American Mathematical Society

The authors study singular perturbations of optimal stochastic control problems and differential games arising in the dimension reduction of system with multiple time scales. They analyze the uniform convergence of the value functions via the associated Hamilton-Jacobi-Bellman-Isaacs equations, in the framework of viscosity solutions. The crucial properties of

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Overview

The authors study singular perturbations of optimal stochastic control problems and differential games arising in the dimension reduction of system with multiple time scales. They analyze the uniform convergence of the value functions via the associated Hamilton-Jacobi-Bellman-Isaacs equations, in the framework of viscosity solutions. The crucial properties of ergodicity and stabilization to a constant that the Hamiltonian must possess are formulated as differential games with ergodic cost criteria. They are studied under various different assumptions and with PDE as well as control-theoretic methods. The authors also construct an explicit example where the convergence is not uniform. Finally they give some applications to the periodic homogenization of Hamilton-Jacobi equations with non-coercive Hamiltonian and of some degenerate parabolic PDEs.

Product Details

ISBN-13:
9780821847152
Publisher:
American Mathematical Society
Publication date:
02/22/2010
Series:
Memoirs of the American Mathematical Society Series, #204
Pages:
77
Product dimensions:
6.80(w) x 9.90(h) x 0.30(d)

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