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Journal Articles SIAM Journal on Control and Optimization Year : 2021

Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems

Abstract

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.

Dates and versions

hal-03264893 , version 1 (18-06-2021)

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Eduardo Abi Jaber, Enzo Miller, Huyen Pham. Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems. SIAM Journal on Control and Optimization, 2021, 59 (2), pp.1581-1603. ⟨10.1137/19M1298287⟩. ⟨hal-03264893⟩
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