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Stochastic Calculus and Applications

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概要 Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and st...ochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."–Zentralblatt (from review of the First Edition).続きを見る
目次 Part I: Measure Theoretic Probability
Measure Integral
Probabilities and Expectation
Part II: Stochastic Processes
Filtrations, Stopping Times and Stochastic Processes
Martingales in Discrete Time
Martingales in Continuous Time
The Classification of Stopping Times
The Progressive, Optional and Predicable -Algebras
Part III: Stochastic Integration
Processes of Finite Variation
The Doob-Meyer Decomposition
The Structure of Square Integrable Martingales
Quadratic Variation and Semimartingales
The Stochastic Integral
Random Measures
Part IV: Stochastic Differential Equations
Ito's Differential Rule
The Exponential Formula and Girsanov's Theorem
Lipschitz Stochastic Differential Equations
Markov Properties of SDEs
Weak Solutions of SDEs
Backward Stochastic Differential Equations
Part V: Applications
Control of a Single Jump
Optimal Control of Drifts and Jump Rates
Filtering. Part VI: Appendices.
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本文を見る Full text available from Springer Mathematics and Statistics eBooks 2015 English/International

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登録日 2020.06.27
更新日 2020.06.28