Stochastic Differential Equations An Introduction with Applications

The main new feature of the fifth edition is the addition of a new chapter, Chapter 12, on applications to mathematical finance. I found it natural to include this material as another major application of stochastic analysis, in view of the amazing development in this field during the last 10-20 yea...

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Hlavní autor: Øksendal, Bernt
Médium: E-kniha
Jazyk:angličtina
Vydáno: Berlin, Heidelberg Springer Berlin Heidelberg 1998
Vydání:Fifth Edition.
Edice:Universitext
Témata:
Calculus of Variations and Optimal Control; Optimization
Differential equations, partial
Distribution (Probability theory
Mathematical optimization
Mathematics
Mathematics and Statistics
Partial Differential Equations
Probability Theory and Stochastic Processes
Systems theory
Systems Theory, Control
Theoretical, Mathematical and Computational Physics
ISBN:9783540637202, 3662036215, 9783662036211, 3540637206
ISSN:0172-5939, 2191-6675
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Obsah:
  • 1. Introduction -- 2. Some Mathematical Preliminaries -- 3. Ito Integrals -- 4. The Ito Formula and the Martingale Representation Theorem -- 5. Stochastic Differential Equations -- 6. The Filtering Problem -- 7. Diffusions: Basic Properties -- 8. Other Topics in Diffusion Theory -- 9. Applications to Boundary Value Problems -- 10. Application to Optimal Stopping -- 11. Application to Stochastic Control -- 12. Application to Mathematical Finance -- Appendix A: Normal Random Variables -- Appendix B: Conditional Expectation -- Appendix C: Uniform Integrability and Martingale Convergence -- Appendix D: An Approximation Result -- Solutions and Additional Hints to Some of the Exercises -- References -- List of Frequently Used Notation and Symbols.