Stochastic calculus and applications
Robert J. Elliott.
New York : Springer-Verlag, ©1982.
viii, 302 págs. ; 25 cm.
Serie: Applications of mathematics ; 18
ISBN: 0387907637
Incluye referencias bibliográficas (p. [295]-298) e índice.
Reseña: MathSciNet, 85b:60059
Contenido
- 1. Conditional expectation. Uniform integrability
- 2. Filtrations, stopping times and stochastic processes
- 3. Martingales: discrete time results
- 4. Martingales: continuous time results
- 5. Predictable and totally inaccessible stopping times
- 6. The optimal and predictable $\sigma$-fields
- 7. Processes of bounded variation
- 8. The Doob-Meyer decomposition
- 9. The structure of square integrable martingales
- 10. Quadratic variation processes
- 11. Stochastic integration with respect to martingales and local martingales
- 12. Semimartingales and the differential rule
- 13. The exponential formula and Girsanov's theorem
- 14. Strong solutions of stochastic differential equations
- 15. Random measures
- 16. The optimal control of a continuous process
- 17. The optimal control of a jump process
- 18. Filtering.