Optimal controls for diffusion in \(R^ d\)- a min-max max-min formula for the minimal cost growth rate
type: Item
instance of: scholarly article
title: Optimal controls for diffusion in \(R^ d\)- a min-max max-min formula for the minimal cost growth rate
zbMATH Open document ID: 0699.49020
DOI: 10.1016/0022-247X(90)90294-P
author: Arie Leizarowitz
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: The infinite horizon optimal control of systems whose dynamics are described by a stochastic differential equation is studied. The expected cost over the [0,T] time interval is assumed to diverge as T tends to infinity, for every control. The following formula is established: \[ \sup_{\phi}\inf_{x}L\phi \leq \alpha \leq \inf_{\phi}\sup_{x}L\phi, \] where L is a second order operator associated with the control problem, and \(\phi\) ranges over a certain class of functions. Existence results for optimal controls are established, assuming the existence of a solution to the infinite horizon H.J.B. equation which satisfies a certain growth condition. Optimal controls are studied both for the long-run average cost and for the overtaking optimality criterion.
Mathematics Subject Classification ID: 49J55
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 4146939
zbMATH Keywords: minimal cost growth rate
zbMATH Keywords: infinite horizon optimal control
zbMATH Keywords: infinite horizon H.J.B. equation
zbMATH Keywords: long-run average cost
zbMATH Keywords: overtaking optimality criterion
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4146939