Probability Essentials

2. Auflage 2004
ISBN: 978-3-540-43871-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 254 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 411 g

Reihe: Universitext

We present here a one semester course on Probability Theory. We also treat measure theory and Lebesgue integration, concentrating on those aspects which are especially germane to the study of Probability Theory. The book is intended to fill a current need: there are mathematically sophisticated students and researchers (especially in Engineering, Economics, and Statistics) who need a proper grounding in Probability in order to pursue their primary interests. Many Probability texts available today are celebrations of Probability Theory, containing treatments of fascinating topics to be sure, but nevertheless they make it difficult to construct a lean one semester course that covers (what we believe) are the essential topics.

Zielgruppe

Research

Autoren/Hrsg.

Protter, Philip

Jacod, Jean

Fachgebiete

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

Inhaltsverzeichnis

1 Introduction.- 2 Axioms of Probability.- 3 Conditional Probability and Independence.- 4 Probabilities on a Finite or Countable Space.- 5 Random Variables on a Countable Space.- 6 Construction of a Probability Measure.- 7 Construction of a Probability Measure on R.- 8 Random Variables.- 9 Integration with Respect to a Probability Measure.- 10 Independent Random Variables.- 11 Probability Distributions on R.- 12 Probability Distributions on Rn.- 13 Characteristic Functions.- 14 Properties of Characteristic Functions.- 15 Sums of Independent Random Variables.- 16 Gaussian Random Variables (The Normal and the Multivariate Normal Distributions).- 17 Convergence of Random Variables.- 18 Weak Convergence.- 19 Weak Convergence and Characteristic Functions.- 20 The Laws of Large Numbers.- 21 The Central Limit Theorem.- 22 L2 and Hilbert Spaces.- 23 Conditional Expectation.- 24 Martingales.- 25 Supermartingales and Submartingales.- 26 Martingale Inequalities.- 27 Martingale Convergence Theorems.- 28 The Radon-Nikodym Theorem.- References.

Über Autor(innen)