Ergodic control problem for one-dimensional diffusions with near-monotone cost
type: Item
instance of: scholarly article
title: Ergodic control problem for one-dimensional diffusions with near-monotone cost
zbMATH Open document ID: 0558.93046
DOI: 10.1016/0167-6911(84)90021-5
author: Alain Bensoussan
author: Vivek Borkar
published in: Systems \& Control Letters
publication date: 1984-01-01T00:00:00Z
review text: This paper deals with the ergodic control of one-dimensional diffusions, governed by controlled stochastic differential equations. From the dynamic programming point of view, the authors derive Bellman's equation of ergodic control. Assuming a near-monotonicity on the cost function and mild conditions on coefficients, they establish the existence and uniqueness of a solution of Bellman's equation and give necessary and sufficient conditions for optimality of a stable Markov control in terms of the equation.
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 49J55
Mathematics Subject Classification ID: 49K45
Mathematics Subject Classification ID: 90C39
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 3891208
zbMATH Keywords: ergodic control
zbMATH Keywords: one-dimensional diffusions
zbMATH Keywords: Bellman's equation
zbMATH Keywords: near- monotonicity
zbMATH Keywords: stable Markov control
reviewed by: Makiko Nisio
MaRDI profile type: Publication
full work available at URL: 0167-6911(84)90021-5
OpenAlex ID: W2047475686
cites work: Existence of Optimal Strategies Based on Specified Information, for a Class of Stochastic Decision Problems
cites work: A note on controlled diffusions on line with time-averaged cost
cites work: Long-term average cost control problems for continuous time Markov processes: A survey
cites work: A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT
description: scientific article; zbMATH DE number 3891208