Stochastic Calculus and Applications

Table of Contents

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   Book Overview
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   Chapter 1 Measure and Integral
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   Chapter 2 Probabilities and Expectation
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   Chapter 3 Filtrations, Stopping Times and Stochastic Processes
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   Chapter 4 Martingales in Discrete Time
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   Chapter 5 Martingales in Continuous Time
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   Chapter 6 The Classification of Stopping Times
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   Chapter 7 The Progressive, Optional and Predictable σ -Algebras
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   Chapter 8 Processes of Finite Variation
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    Chapter 9 The Doob–Meyer Decomposition
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    Chapter 10 The Structure of Square Integrable Martingales
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    Chapter 11 Quadratic Variation and Semimartingales
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    Chapter 12 The Stochastic Integral
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    Chapter 13 Random Measures
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    Chapter 14 Itô’s Differential Rule
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    Chapter 15 The Exponential Formula and Girsanov’s Theorem
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    Chapter 16 Lipschitz Stochastic Differential Equations
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    Chapter 17 Markov Properties of SDEs
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    Chapter 18 Weak Solutions of SDEs
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    Chapter 19 Backward Stochastic Differential Equations
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    Chapter 20 Control of a Single Jump
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    Chapter 21 Optimal Control of Drifts and Jump Rates
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    Chapter 22 Filtering