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An Auxiliary Equation for the Bellman Equation in a One-Dimensional Ergodic Control

Journal Article · · Applied Mathematics and Optimization
DOI:https://doi.org/10.1007/S002450010022· OSTI ID:21067509
 [1]
  1. Department of Mathematics, Faculty of Science, Toyama University, Toyama 930-8555 (Japan)
In this paper we consider the Bellman equation in a one-dimensional ergodic control. Our aim is to show the existence and the uniqueness of its solution under general assumptions. For this purpose we introduce an auxiliary equation whose solution gives the invariant measure of the diffusion corresponding to an optimal control. Using this solution, we construct a solution to the Bellman equation. Our method of using this auxiliary equation has two advantages in the one-dimensional case. First, we can solve the Bellman equation under general assumptions. Second, this auxiliary equation gives an optimal Markov control explicitly in many examples.
OSTI ID:
21067509
Journal Information:
Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 43; ISSN 0095-4616
Country of Publication:
United States
Language:
English

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