Integral operator riccati equations arising in stochastic volterra control problems

Eduardo Abi Jaber; Enzo Miller; Huyen Pham

doi:10.1137/19M1298287

Integral operator riccati equations arising in stochastic volterra control problems

Eduardo Abi Jaber
, Enzo Miller
, Huyen Pham

Université Panthéon-Sorbonne (Paris 1)
Laboratoire de Probabilités et Modèles Aléatoires

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We establish existence and uniqueness for infinite-dimensional Riccati equations taking values in the Banach space L¹(μ ⊗ μ ) for certain signed matrix measures μ which are not necessarily finite. Such equations can be seen as the infinite-dimensional analogue of matrix Riccati equations, and they appear in the linear-quadratic control theory of stochastic Volterra equations.

langue originale	Anglais
Pages (de - à)	1581-1603
Nombre de pages	23
journal	SIAM Journal on Control and Optimization
Volume	59
Numéro de publication	2
Les DOIs	https://doi.org/10.1137/19M1298287
état	Publié - 1 janv. 2021
Modification externe	Oui

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10.1137/19M1298287

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abstract = "We establish existence and uniqueness for infinite-dimensional Riccati equations taking values in the Banach space L1(μ ⊗ μ ) for certain signed matrix measures μ which are not necessarily finite. Such equations can be seen as the infinite-dimensional analogue of matrix Riccati equations, and they appear in the linear-quadratic control theory of stochastic Volterra equations.",

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AU - Pham, Huyen

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N2 - We establish existence and uniqueness for infinite-dimensional Riccati equations taking values in the Banach space L1(μ ⊗ μ ) for certain signed matrix measures μ which are not necessarily finite. Such equations can be seen as the infinite-dimensional analogue of matrix Riccati equations, and they appear in the linear-quadratic control theory of stochastic Volterra equations.

AB - We establish existence and uniqueness for infinite-dimensional Riccati equations taking values in the Banach space L1(μ ⊗ μ ) for certain signed matrix measures μ which are not necessarily finite. Such equations can be seen as the infinite-dimensional analogue of matrix Riccati equations, and they appear in the linear-quadratic control theory of stochastic Volterra equations.

KW - Infinite-dimensional Lyapunov equation

KW - Integral operator Riccati equation

KW - Linear-quadratic control

KW - Stochastic Volterra equations

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DO - 10.1137/19M1298287

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Integral operator riccati equations arising in stochastic volterra control problems

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