Optimal Feedback for Stochastic Linear Quadratic Control and Backward Stochastic Riccati Equations in Infinite Dimensions

Xu Zhang, Qi Lu

ISBN 10: 1470468751 / ISBN 13: 9781470468750

Verlag: American Mathematical Society, US, 2024

Beschreibung

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.

Bestandsnummer des Verkäufers LU-9781470468750

Bibliografische Details

• Titel: Optimal Feedback for Stochastic Linear Quadratic Control and Backward Stochastic Riccati Equations in Infinite Dimensions
• Verlag: American Mathematical Society, US
• Erscheinungsjahr: 2024
• Sprache: Englisch
• ISBN-10: 1470468751
• ISBN-13: 9781470468750
• Einband: Paperback
• Zustand: New
• Gewicht: 157 Gramm

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

Qi Lu, Sichuan University, Chengdu, People's Republic of China.

Xu Zhang, Sichuan University, Chengdu, People's Republic of China.