After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.
After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Horst Osswald is a Professor of Mathematics at Universität München.
Inhaltsangabe
Part I. The Fundamental Principles: 1. Preface 2. Martingales 3. Fourier and Laplace transformations 4. Abstract Wiener-Fréchet spaces 5. Two concepts of no-anticipation in time 6. Malliavin calculus on the space of real sequences 7. Introduction to poly-saturated models of mathematics 8. Extension of the real numbers and properties 9. Topology 10. Measure and integration on Loeb spaces Part II. An Introduction to Finite- and Infinite-Dimensional Stochastic Analysis: 11. From finite- to infinite-dimensional Brownian motion 12. The Itô integral for infinite-dimensional Brownian motion 13. The iterated integral 14. Infinite-dimensional Ornstein-Uhlenbeck processes 15. Lindstrøm's construction of standard Lévy processes from discrete ones 16. Stochastic integration for Lévy processes Part III. Malliavin Calculus: 17. Chaos decomposition 18. The Malliavin derivative 19. The Skorokhod integral 20. The interplay between derivative and integral 21. Skorokhod integral processes 22. Girsanov transformation 23. Malliavin calculus for Lévy processes Appendix A. Poly-saturated models Appendix B. The existence of poly-saturated models References Index.
Part I. The Fundamental Principles: 1. Preface 2. Martingales 3. Fourier and Laplace transformations 4. Abstract Wiener-Fréchet spaces 5. Two concepts of no-anticipation in time 6. Malliavin calculus on the space of real sequences 7. Introduction to poly-saturated models of mathematics 8. Extension of the real numbers and properties 9. Topology 10. Measure and integration on Loeb spaces Part II. An Introduction to Finite- and Infinite-Dimensional Stochastic Analysis: 11. From finite- to infinite-dimensional Brownian motion 12. The Itô integral for infinite-dimensional Brownian motion 13. The iterated integral 14. Infinite-dimensional Ornstein-Uhlenbeck processes 15. Lindstrøm's construction of standard Lévy processes from discrete ones 16. Stochastic integration for Lévy processes Part III. Malliavin Calculus: 17. Chaos decomposition 18. The Malliavin derivative 19. The Skorokhod integral 20. The interplay between derivative and integral 21. Skorokhod integral processes 22. Girsanov transformation 23. Malliavin calculus for Lévy processes Appendix A. Poly-saturated models Appendix B. The existence of poly-saturated models References Index.
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