# A Linear PDE Approach to the Bellman Equation of Ergodic Control with Periodic Structure

A Linear PDE Approach to the Bellman Equation of Ergodic Control with Periodic Structure Abstract. In this paper we give a new proof of the existence result of Bensoussan [1, Theorem II-6.1] for the Bellman equation of ergodic control with periodic structure. This Bellman equation is a nonlinear PDE, and he constructed its solution by using the solution of a nonlinear PDE. On the contrary, our key idea is to solve two linear PDEs. Hence, we propose a linear PDE approach to this Bellman equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# A Linear PDE Approach to the Bellman Equation of Ergodic Control with Periodic Structure

, Volume 47 (2) – Mar 12, 2003
7 pages

/lp/springer_journal/a-linear-pde-approach-to-the-bellman-equation-of-ergodic-control-with-GveoNsOurS
Publisher
Springer-Verlag
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-002-0758-y
Publisher site
See Article on Publisher Site

### Abstract

Abstract. In this paper we give a new proof of the existence result of Bensoussan [1, Theorem II-6.1] for the Bellman equation of ergodic control with periodic structure. This Bellman equation is a nonlinear PDE, and he constructed its solution by using the solution of a nonlinear PDE. On the contrary, our key idea is to solve two linear PDEs. Hence, we propose a linear PDE approach to this Bellman equation.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Mar 12, 2003

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