Stochastic Calculus and Applications

• Κύριοι συγγραφείς: Cohen, Samuel N. (Συγγραφέας), Elliott, Robert J. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York : Imprint: Birkhäuser, 2015.
• Έκδοση: 2nd ed. 2015.
• Σειρά: Probability and Its Applications,
• Θέματα: Mathematics.; Partial differential equations.; Economics, Mathematical.; Computer mathematics.; Probabilities.; Electrical engineering.; Probability Theory and Stochastic Processes.; Partial Differential Equations.; Electrical Engineering.; Computational Mathematics and Numerical Analysis.; Quantitative Finance.

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 stochastic integrals as used by systems theorists, electronic engineers and, more recently, those work...

Πίνακας περιεχομένων:

• 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.