Author | Jacobs, Konrad. author |
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Title | Discrete Stochastics [electronic resource] / by Konrad Jacobs |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1992 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8645-1 |
Descript | X, 283 p. online resource |
I. Introduction -- 1. Encountering Random -- 2. Specimens of Stochastic Reasoning -- II. Markovian Dynamics -- 1. Finite-state Markovian dynamical systems -- 2. The convex set of stochastic matrices -- 3. The asymptotic behavior of Pn: some special cases -- 4. Asymptotic behavior of P, P2,...: the method of invariant sets -- III. Discrete Probability Spaces -- 1. The Notion of a Discrete Probability Space (DPS) -- 2. Obtaining New Probability Spaces from Given Ones -- 3. Independence -- IV. Independent Identically Distributed (IID) Random Variables -- 1. Addition of independent RVs -- 2. Expectation and Variance -- 3. The Weak Law of Large Numbers (WLLN) -- 4. The Central Limit Theorem (CLT) I -- 5. The Central Limit Theorem (CLT) II -- 6. Outlook -- V. Statistics -- 1. Specimens of Statistical Reasoning -- 2. The Game-Theoretical Framework of Statistical Theory -- 3. Tests -- 4. Outlook -- VI. Markov Processes -- 1. Conditional Probabilities -- 2. Markov Processes -- VII. Elements of Information Theory -- 1. Combinatorial and Algebraic Coding Theory -- 2. Source Coding -- 3. Noisy Channels -- VIII. Fluctuation Theory -- 1. The Combinatorial Arcsin Law of Erik Sparre Andersen -- 2. Arcsin -- 3. Symmetrically Distributed Random Variables -- 4. Fluctuations of Random Walks -- 5. The Andersen-Spitzer Formula -- 6. Outlook -- IX. Optimal Strategies in Casinoes: Red and Black -- 1. Strategies and Their Probability of Success -- 2. Some Properties of BOLD -- 3. The Optimality of BOLD for p ? 1/2 ? r -- 4. Non-Optimality of BOLD if p ? 1/2 ? r Fails -- X. Foundational Problems -- 1. The Theory of Randomness -- 2. Subjective Probabilities -- 3. Belief (โbelโ) Functions -- Appendix A: The Marriage Theorem -- Appendix B: Markovian Semigroups -- Appendix C: One-parameter semigroups of stochastic matrices