Necessary conditions of optimality for some stochastic integrodifferential equations of neutral type on Hilbert spaces
type: Item
instance of: scholarly article
title: Necessary conditions of optimality for some stochastic integrodifferential equations of neutral type on Hilbert spaces
zbMATH Open document ID: 1394.49023
author: Moustapha Dieye
author: Mamadou Abdoul Diop
author: Khalil Ezzinbi
published in: Applied Mathematics and Optimization
publication date: 2018-05-31T00:00:00Z
review text: The authors consider partially observed control problems governed by stochastic integrodifferential equations of neutral type on Hilbert spaces driven by relaxed controls. Under some conditions, the existence and the uniquenes of mild solution which has a continuous modification are established. The continuity of the map \(u \mapsto x\), that is, the control to the solution map (endowed with certain weak topology) is proved. The authors also consider an optimal control problem of Bolza type. Using the above results they give necessary conditions of optimality for a class of stochastic integrodifferential equations of neutral type on Hilbert spaces. An example is given to illustrate the results.
Mathematics Subject Classification ID: 49K45
Mathematics Subject Classification ID: 49K21
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49K05
Mathematics Subject Classification ID: 47G20
Mathematics Subject Classification ID: 60H20
zbMATH DE Number: 6877185
zbMATH Keywords: integrodifferential equations
zbMATH Keywords: neutral type
zbMATH Keywords: resolvent operator
zbMATH Keywords: mild solutions
zbMATH Keywords: Hilbert spaces
zbMATH Keywords: relaxed controls
zbMATH Keywords: optimal control
zbMATH Keywords: necessary conditions
MaRDI profile type: Publication
full work available at URL: s00245-016-9377-x
OpenAlex ID: W2523920408
cites work: Q3997711
cites work: Q5471326
cites work: Q5324581
cites work: Stochastic evolution equations on Hilbert spaces with partially observed relaxed controls and their necessary conditions \\ of optimality
cites work: Q3193086
cites work: Stochastic neutral evolution equations on Hilbert spaces with partially observed relaxed control and their necessary conditions of optimality
cites work: Stochastic minimum principle for partially observed systems subject to continuous and jump diffusion processes and driven by relaxed controls
cites work: Q3172269
cites work: Q3925435
cites work: Q4811484
cites work: Necessary and Sufficient Optimality Conditions for Relaxed and Strict Control Problems
cites work: Q4743352
cites work: Stochastic Equations in Infinite Dimensions
cites work: Existence and uniqueness of mild solutions to some neutral stochastic partial functional integrodifferential equations with non-Lipschitz coefficients
cites work: Existence and regularity of solutions for neutral partial functional integrodifferential equations
cites work: Q4355647
cites work: Resolvent Operators for Integral Equations in a Banach Space
cites work: Analytic resolvent operators for integral equations in Banach space
cites work: Stability of semilinear stochastic evolution equations
cites work: Q5533878
cites work: A General Stochastic Maximum Principle for Optimal Control Problems
cites work: The maximum principle for a jump-diffusion mean-field model and its application to the mean-variance problem
DOI: 10.1007/S00245-016-9377-X
description: scientific article; zbMATH DE number 6877185