This second edition presents up-to-date material on the theory of weak convergance of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their applications to products of random matrices. In addition, this unique work examines the essentials of abstract semigroup theory and its application to concrete semigroups of matrices. This substantially revised text includes exercises at various levels at the end of each section and includes the best available proofs on the most important theorems used in a book, making it suitable for a one semester course on semigroups. In addition, it could also be used as a main text or supplementary material for courses focusing on probability on algebraic structures or weak convergance. This book is ideally suited to graduate students in mathematics, and students in other fields, such as engineering and the sciences with an interest in probability. Students in statistics using advanced probability will also find this book useful Introduction.- Axioms of Probability.- Conditional Probability and Independence.- Probabilities on a Countable Space.- Random Variables on a Countable Space.- Construction of a Probability Measure.- Construction of a Probability Measure on R.- Random Variables.- Integration with Respect to a Probability Measure.- Independent Random Variables.- Probability Distributions on R.- Probability Distributions on Rn.- Characteristic Functions.- Properties of Characteristic Functions.- Sums of Independent Random Variables.- Gaussian Random Variables (The Normal and the Multivariate Normal Distributions).- Convergence of Random Variables; Weak Convergence.- Weak Convergence and Characteristic Functions.- The Laws of Large Numbers.- The Central Limit Theorem.- L2 and Hilbert Spaces.- Conditional Expectation.- Martingales.- Supermartingales and Submartingales.- Martingale Inequalities.- Martingale Convergence Theorems.- The Radon-Nikodym Theorem
Probability essentials
扫码加好友，拉您进群
全部版块
我的主页
收藏
