Stochastic Control by Functional Analysis Methods
Published on 18. August 2011
409 pages
978-0-08-087532-3 (ISBN)
Description
Stochastic Control by Functional Analysis Methods
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04/2000
North-Holland
€107.70
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Content
- Front Cover
- Stochastic Control by Functional Analysis Methods
- Copyright Page
- Contents
- CHAPTER I. STOCHASTIC CALCULUS AND STOCHASTIC DIFFERENTIAL EQUATIONS
- INTRODUCTION
- 1. PRELIMINARIES
- 2. STOCHASTIC INTEGRALS
- 3. ITO's FORMULA
- 4. STOCHASTIC DIFFERENTIAL EQUATIONS
- 5. GIRSANOV TRANSFORMATION
- CHAPTER II. PARTIAL DIFFERENTIAL EQUATIONS
- INTRODUCTION
- 1. FUNCTIONAL SPACES
- 2. THE DIRICHLET PROBLEM FOR ELLIPTIC EQUATIONS
- 3. PARABOLIC EQUATIONS
- CHAPTER III. MARTINGALE PROBLEM
- INTRODUCTION
- 1. PROPERTIES OF CONTINUOUS MARTINGALES
- 2. DEFINITION OF THE MARTINGALE PROBLEM
- 3. EXISTENCE AND UNIQUENESS OF THE SOLUTION OF THE MARTINGALE PROBLEM
- 4. INTERPRETATION OF THE SOLUTION OF P.D.E.
- 5. SEMI GROUPS
- CHAPTER IV. STOCHASTIC CONTROL WITH COMPLETE INFORMATION
- INTRODUCTION
- 1. SETTING OF THE PROBLEM
- 2. THE EQUATION OF DYNAMIC PROGRAMMING
- 3. SOLUTION OF THE STOCHASTIC CONTROL PROBLEM
- 4. EVOLUTION PROBLEMS
- 5. SEMI GROUP FORMULATION
- CHAPTER V. FILTERING AND PREDICTION FOR LINEAR S.D.E.
- INTRODUCTION
- 1. SETTING OF THE PROBLEM
- 2. CHARACTERIZATION OF THE BEST ESTIMATE
- 3. RECURSIVITY - KALMAN FILTER
- 4. PREDICTION
- CHAPTER VI. VARIATIONAL METHODS IN STOCHASTIC CONTROL
- INTRODUCTION
- 1. MODEL WITH ADDITIVE NOISE
- 2. THE CASE WITH INCOMPLETE OBSERVATION
- 3. SEPARATION PRINCIPLE
- CHAPTER VII. PROBLEMS OF OPTIMAL STOPPING
- INTRODUCTION
- 1. SETTING OF THE PROBLEM
- 2. UNILATERAL PROBLEMS
- 3. VARIATIONAL INEQUALITIES
- 4. SOLUTION OF THE OPTIMAL STOPPING TIME PROBLEM
- 5. SEMI GROUP APPROACH
- 6. INTERPRETATION AS A PROBLEM OF OPTIMAL STOPPING
- CHAPTER VIII. IMPULSIVE CONTROL
- INTRODUCTION
- 1. SETTING OF THE PROBLEM
- 2. QUASI VARIATIONAL INEQUALITIES
- 3. SOLUTION OF THE IMPULSIVE CONTROL PROBLEM
- 4. SEMI GROUP APPROACH
- REFERENCES
