Optimal feedback for stochastic linear quadratic control and backward stochastic Riccati equations in infinite dimensions
著者
書誌事項
Optimal feedback for stochastic linear quadratic control and backward stochastic Riccati equations in infinite dimensions
（Memoirs of the American Mathematical Society, no. 1467）
American Mathematical Society, c2024
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注記
"February 2024, volume 294, number 1467 (fourth of 5 numbers)"
Includes bibliographical references (p. 103-107)
内容説明・目次
内容説明
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.
目次
1. 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 SPDEs
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