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2021
- handle: 10670/1.kgugwo
- hal: hal-03264893
- ARXIV: 1911.01903v1
- doi: 10.1137/19M1298287
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info:eu-repo/semantics/altIdentifier/arxiv/1911.01903v1
Ce document est lié à :
info:eu-repo/semantics/altIdentifier/doi/10.1137/19M1298287
Mots-clés
infinite-dimensional Lyapunov equation integral operator Riccati equation linear-quadratic control stochastic Volterra equations AMS Subject Headings : 47G10, 49N10, 34G20Sujets proches
Equations, VolterraCiter ce document
Eduardo Abi Jaber et al., « Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems », HAL-SHS : économie et finance, ID : 10.1137/19M1298287
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Résumé
We establish existence and uniqueness for infinite-dimensional Riccati equations taking values in the Banach space $L^1(\mu \otimes \mu)$ for certain signed matrix measures $\mu$ 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.