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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1581-1603
Number of pages	23
Journal	SIAM Journal on Control and Optimization
Volume	59
Issue number	2
DOIs	https://doi.org/10.1137/19M1298287
Publication status	Published - 1 Jan 2021
Externally published	Yes

Keywords

Infinite-dimensional Lyapunov equation
Integral operator Riccati equation
Linear-quadratic control
Stochastic Volterra equations

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10.1137/19M1298287

Cite this

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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 - Miller, Enzo

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

U2 - 10.1137/19M1298287

DO - 10.1137/19M1298287

M3 - Article

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JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

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Integral operator riccati equations arising in stochastic volterra control problems

Abstract

Keywords

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