Free Delivery Over $100
|
|
|||
|
||||
OverviewIt 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. Full Product DetailsAuthor: Qi Lu , Xu ZhangPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: Volume: 294 Number: 1467 ISBN: 9781470468750ISBN 10: 1470468751 Pages: 107 Publication Date: 31 May 2024 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents1. Introduction 2. Statement of the main results 3. Some preliminary results 4. Proof of the first main result 5. Proof of the second main result 6. Existence of transposition solutions to some operator-valued BSREs 7. Some examples of controlled SPDEsReviewsAuthor InformationQi Lu, Sichuan University, Chengdu, People's Republic of China. Xu Zhang, Sichuan University, Chengdu, People's Republic of China. Tab Content 6Author Website:Countries AvailableAll regions |
||||
