Integral operator Riccati equations arising in stochastic Volterra control problems
Résumé
We establish existence and uniqueness for infinite dimensional Riccati equations taking values in the Banach space L 1 (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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