## Differential and Integral Equations

### A comparison theorem for Bellman equations of ergodic control

#### Abstract

The aim of this paper is to establish a comparison theorem for the Bellman equation of an ergodic control in $\mathbb R ^d$. This comparison theorem gives a new characterization of the optimal value by sub/super--solutions of the Bellman equation. This result is applicable to compute both of lower and upper bound of the optimal value. Furthermore, from this comparison theorem, we also give a simple proof of the uniqueness result for the Bellman equation.

#### Article information

Source
Differential Integral Equations, Volume 16, Number 6 (2003), 641-651.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356060604

Mathematical Reviews number (MathSciNet)
MR1973272

Zentralblatt MATH identifier
1051.93098

Subjects
Primary: 93E20: Optimal stochastic control
Secondary: 49L20: Dynamic programming method

#### Citation

Fujita, Yasuhiro; Ohmori, Katsushi. A comparison theorem for Bellman equations of ergodic control. Differential Integral Equations 16 (2003), no. 6, 641--651. https://projecteuclid.org/euclid.die/1356060604