Controlled Markov processes and viscosity solutions (eBook, 2006) []
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Controlled Markov processes and viscosity solutions

Author: Wendell H Fleming; H Mete Soner
Publisher: New York : Springer, ©2006.
Series: Applications of mathematics, 25.
Edition/Format:   eBook : Document : English : 2nd edView all editions and formats
"This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. Stochastic control problems are treated using the dynamic programming approach. The authors approach stochastic control problems by the method of dynamic programming."--Jacket

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Genre/Form: Electronic books
Additional Physical Format: Print version:
Fleming, Wendell Helms, 1928-
Controlled Markov processes and viscosity solutions.
New York : Springer, ©2006
(DLC) 2005929857
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Wendell H Fleming; H Mete Soner
ISBN: 0387260455 9780387260457 0387310711 9780387310718 6610461996 9786610461998
OCLC Number: 228397047
Description: 1 online resource (428 pages)
Contents: Cover --
Contents --
Preface to Second Edition --
Preface --
Notation --
I Deterministic Optimal Control --
I.1 Introduction --
I.2 Examples --
I.3 Finite time horizon problems --
I.4 Dynamic programming principle --
I.5 Dynamic programming equation --
I.6 Dynamic programming and Pontryagin's principle. --
I.7 Discounted cost with infinite horizon --
I.8 Calculus of variations I --
I.9 Calculus of variations II --
I.10 Generalized solutions to Hamilton-Jacobi equations --
I.11 Existence theorems --
I.12 Historical remarks --
II Viscosity Solutions --
II. 1 Introduction --
II. 2 Examples --
II. 3 An abstract dynamic programming principle --
II. 4 Definition --
II. 5 Dynamic programming and viscosity property --
II. 6 Properties of viscosity solutions --
II. 7 Deterministic optimal control and viscosity solutions --
II. 8 Viscosity solutions: first order case --
II. 9 Uniqueness: first order case --
II. 10 Continuity of the value function --
II. 11 Discounted cost with infinite horizon --
II. 12 State constraint --
II. 13 Discussion of boundary conditions --
II. 14 Uniqueness: first-order case --
II. 15 Pontryagin's maximum principle (continued) --
II. 16 Historical remarks --
III Optimal Control of Markov Processes: Classical Solutions --
III. 1 Introduction --
III. 2 Markov processes and their evolution operators --
III. 3 Autonomous (time-homogeneous) Markov processes --
III. 4 Classes of Markov processes --
III. 5 Markov diffusion processes on IRn; stochastic differential equations --
III. 6 Controlled Markov processes --
III. 7 Dynamic programming: formal description --
III. 8 A Verification Theorem; finite time horizon --
III. 9 Infinite Time Horizon --
III. 10 Viscosity solutions --
III. 11 Historical remarks --
IV Controlled Markov Diffusions in IRn --
IV. 1 Introduction --
IV. 2 Finite time horizon problem --
IV. 3 Hamilton-Jacobi-Bellman PDE --
IV. 4 Uniformly parabolic case --
IV. 5 Infinite time horizon --
IV. 6 Fixed finite time horizon problem: Preliminary estimates --
IV. 7 Dynamic programming principle --
IV. 8 Estimates for first order difference quotients --
IV. 9 Estimates for second-order difference quotients --
IV. 10 Generalized subsolutions and solutions --
IV. 11 Historical remarks --
V Viscosity Solutions: Second-Order Case --
V.1 Introduction --
V.2 Dynamic programming principle --
V.3 Viscosity property --
V.4 An equivalent formulation --
V.5 Semiconvex, concave approximations --
V.6 Crandall-Ishii Lemma --
V.7 Properties of H --
V.8 Comparison --
V.9 Viscosity solutions in Q0 --
V.10 Historical remarks --
VI Logarithmic Transformations and Risk Sensitivity --
VI. 1 Introduction --
VI. 2 Risk sensitivity --
VI. 3 Logarithmic transformations for Markov diffusions --
VI. 4 Auxiliary stochastic control problem --
VI. 5 Bounded region Q --
VI. 6 Small noise limits --
VI. 7 H-infinity norm of a nonlinear system --
VI. 8 Risk sensitive control --
VI. 9 Logarithmic transformations for Markov processes --
VI. 10 Historical remarks --
VII Singular Perturbations --
VII. 1 Introduction --
VII. 2 Examples --
VII. 3 Barles and Perthame procedur
Series Title: Applications of mathematics, 25.
Responsibility: Wendell H. Fleming, H. Mete Soner.


This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. New chapters in this second edition introduce the role of  Read more...


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