Probability

Erscheinungsjahr 1992
ISBN: 978-0-89871-296-4
Verlag: Society for Industrial and Applied Mathematics

Buch, Englisch, Band 7, 435 Seiten, Format (B × H): 154 mm x 234 mm, Gewicht: 610 g

Reihe: Classics in Applied Mathematics

Well known for the clear, inductive nature of its exposition, this reprint volume is an excellent introduction to mathematical probability theory. It may be used as a graduate-level text in one- or two-semester courses in probability for students who are familiar with basic measure theory, or as a supplement in courses in stochastic processes or mathematical statistics. Designed around the needs of the student, this book achieves readability and clarity by giving the most important results in each area while not dwelling on any one subject. Each new idea or concept is introduced from an intuitive, common-sense point of view. Students are helped to understand why things work, instead of being given a dry theorem-proof regime.

Autoren/Hrsg.

Breiman, Leo

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

1. Introduction; 2. Mathematical framework; 3. Independence; 4. Conditional probability and conditional expectation; 5. Martingales; 6. Stationary processes and the ergodic theorem; 7. Markov chains; 8. Convergence in distribution and the tools thereof; 9. The one-dimensional central limit problem; 10. The renewal theorem and local limit theorem; 11. Multidimensional central limit theorem and Gaussian processes; 12. Stochastic processes and Brownian motion; 13. Invariance theorems; 14. Martingales and processes with stationary, independent increments; 15. Markov processes, introduction and pure jump case; 16. Diffusions; Appendix; Bibliography; Index.