Author | Berger, Marc A. author |
---|---|
Title | An Introduction to Probability and Stochastic Processes [electronic resource] / by Marc A. Berger |
Imprint | New York, NY : Springer New York, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2726-7 |
Descript | XII, 205 p. online resource |
I. Univariate Random Variables -- Discrete Random Variables -- Properties of Expectation -- Properties of Characteristic Functions -- Basic Distributions -- Absolutely Continuous Random Variables -- Basic Distributions -- Distribution Functions -- Computer Generation of Random Variables -- Exercises -- II. Multivariate Random Variables -- Joint Random Variables -- Conditional Expectation -- Orthogonal Projections -- Joint Normal Distribution -- Multi-Dimensional Distribution Functions -- Exercises -- III. Limit Laws -- Law of Large Numbers -- Weak Convergence -- Bochnerโs Theorem -- Extremes -- Extremal Distributions -- Large Deviations -- Exercises -- IV. Markov ChainsโPassage Phenomena -- First Notions and Results -- Limiting Diffusions -- Branching Chains -- Queueing Chains -- Exercises -- V. Markov ChainsโStationary Distributions and Steady State -- Stationary Distributions -- Geometric Ergodicity -- Examples -- Exercises -- VI. Markov Jump Processes -- Pure Jump Processes -- Poisson Process -- Birth and Death Process -- Exercises -- VII. Ergodic Theory with an Application to Fractals -- Ergodic Theorems -- Subadditive Ergodic Theorem -- Products of Random Matrices -- Oseledecโs Theorem -- Fractals -- Bibliographical Comments -- Exercises -- References -- Solutions (Sections IโV)