Author | Jacod, Jean. author |
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Title | Probability Essentials [electronic resource] / by Jean Jacod, Philip Protter |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-3-642-55682-1 |
Descript | X, 254 p. online resource |
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