Optimal Feedback for Stochastic Linear Quadratic Control and Backward Stochastic Riccati Equations in Infinite Dimensions: Volume: 294 Number: 1467 (Memoirs of the American Mathematical Society)

Lu, Qi (Author)/ Zhang, Xu (Author)

ISBN 10: 1470468751 / ISBN 13: 9781470468750

Editore: American Mathematical Society, 2024

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107 pages. In Stock. Codice articolo __1470468751

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Titolo: Optimal Feedback for Stochastic Linear ...

Casa editrice: American Mathematical Society

Data di pubblicazione: 2024

Legatura: Paperback

Condizione: Brand New

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Riassunto:

It is a longstanding unsolved problem to characterize the optimal feedbacks for general SLQs (i.e., stochastic linear quadratic control problems) with random coefficients in infinite dimensions; while the same problem but in finite dimensions was just addressed very recently. This paper is devoted to giving a solution to this problem under some assumptions which can be verified for interesting concrete models. More precisely, under these assumptions, we establish the equivalence between the existence of optimal feedback operator for infinite dimensional SLQs and the solvability of the corresponding operator-valued, backward stochastic Riccati equations. A key contribution of this work is to introduce a suitable notion of solutions (i.e., transposition solutions to the aforementioned Riccati equations), which plays a crucial role in both the statement and the proof of our main results.