General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions

The classical Pontryagin maximum principle (addressed to deterministic finite dimensional control systems) is one of the three milestones in modern control theory. The corresponding theory is by now well-developed in the deterministic infinite dimensional setting and for the stochastic differential equations. However, very little is known about the same problem but for controlled stochastic (infinite dimensional) evolution equations when the diffusion term contains the control variables and the control domains are allowed to be non-convex. Indeed, it is one of the longstanding unsolved problems in stochastic control theory to establish the Pontryagin type maximum principle for this kind of general control systems: this book aims to give a solution to this problem. This book will be useful for both beginners and experts who are interested in optimal control theory for stochastic evolution equations.

List of contents

1 Introduction.- 2 Preliminaries.- 3 Well-posedness of the vector-valued BSEEs.- 4 Well-posedness result for the operator-valued BSEEs with special data.- 5 Sequential Banach-Alaoglu-type theorems in the operator version.- 6 Well-posedness of the operator-valued BSEEs in the general case.- 7 Some properties of the relaxed transposition solutions to the operator-valued BSEEs.- 8 Necessary condition for optimal controls, the case of convex control domains.- 9 Necessary condition for optimal controls, the case of non-convex control domains.

Product details

• Authors: Qi Lü, Xu Zhang
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 24.06.2014
• EAN: 9783319066318
• ISBN: 978-3-31-906631-8
• No. of pages: 146
• Dimensions: 158 mm x 236 mm x 11 mm
• Weight: 248 g
• Illustrations: IX, 146 p. 1 illus. in color.
• Series: SpringerBriefs in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; C, Optimization, Statistics, Mathematics and Statistics, Finance & accounting, Probability Theory and Stochastic Processes, Systems Theory, Control, Probability & statistics, Probabilities, Stochastics, Probability Theory, Applied mathematics, Economics, Mathematical, Quantitative Finance, Mathematics in Business, Economics and Finance, Calculus of Variations and Optimization, Calculus of variations, Calculus of Variations and Optimal Control; Optimization, Statistics, general, System Theory, Economics, finance, business and management