Direct solution of a Riccati equation arising in stochastic control theory
type: Item
instance of: scholarly article
title: Direct solution of a Riccati equation arising in stochastic control theory
zbMATH Open document ID: 0555.93070
DOI: 10.1007/BF01442178
author: Guiseppe Da Prato
published in: Applied Mathematics and Optimization
publication date: 1984-01-01T00:00:00Z
review text: The main result of the paper is that of existence and uniqueness for the Riccati equation, which arises in the solution of an abstract linear stochastic optimal control problem with a quadratic cost functional; the system is posed on a Hilbert space and the system operator and the noise operator are both unbounded. The solution to the control problem then follows by the usual dynamic programming arguments [\textit{A. Ichikawa}, SIAM J. Control Optimization 17, 152-174 (1979; Zbl 0434.93069)].
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 46C99
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 90C39
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 3885779
zbMATH Keywords: Riccati equation
zbMATH Keywords: stochastic optimal control
zbMATH Keywords: Hilbert space
MaRDI profile type: Publication
cites work: Q4746091
cites work: Ito's lemma in infinite dimensions
cites work: Stochastic differential equations in Hilbert space
cites work: Q3668594
cites work: Some results on linear stochastic evolution equations in hilbert spaces by the semi–groups method
cites work: Maximal regularity for evolution equations by interpolation and extrapolation
cites work: Q4751266
cites work: Dynamic Programming Approach to Stochastic Evolution Equations
cites work: On a stopped Doob's inequality and general stochastic equations
cites work: Sur l'étude directe d'équations non linéaires intervenant en théorie du contrôle optimal
cites work: Q5332803
full work available at URL: https://doi.org/10.1007/bf01442178
OpenAlex ID: W2134065371
description: scientific article; zbMATH DE number 3885779