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https://hdl.handle.net/2440/113997
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Type: | Journal article |
Title: | On the existence of optimal controls for backward stochastic partial differential equations |
Author: | Meng, Q. Shen, Y. Shi, P. |
Citation: | Statistics and Probability Letters, 2018; 137:113-123 |
Publisher: | Elsevier BV |
Issue Date: | 2018 |
ISSN: | 0167-7152 1879-2103 |
Statement of Responsibility: | Qingxin Meng, Yang Shen, Peng Shi |
Abstract: | This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward stochastic evolution equations. Under some growth and monotonicity conditions on the coefficients and suitable assumptions on the Hamiltonian, the existence of the optimal control boils down to proving the uniqueness and existence of a solution to the stochastic Hamiltonian system, i.e. a fully coupled forward–backward stochastic evolution equation. Using some a prior estimates, we prove the uniqueness and existence of the solution via the method of continuation. Two examples of linear–quadratic control are solved to demonstrate our results. |
Keywords: | Backward stochastic partial differential equations; forward–backward stochastic evolution equations; infinite dimensions; uniqueness and existence; maximum principle |
Description: | Available online 2 February 2018 |
Rights: | © 2018 Elsevier B.V. All rights reserved. |
DOI: | 10.1016/j.spl.2018.01.013 |
Grant ID: | http://purl.org/au-research/grants/arc/DP170102644 B12018 B17048 B17017 11101140 11301177 61174058 60974052 61134001 61773131 U1509217 2011M500721 2012T50391 |
Published version: | http://dx.doi.org/10.1016/j.spl.2018.01.013 |
Appears in Collections: | Aurora harvest 8 Electrical and Electronic Engineering publications |
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