{"product_id":"discrete-stochastics-konrad-jacobs-9783764325916","title":"Discrete Stochastics","description":"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 (\"bel\") Functions.- Appendix A: The Marriage Theorem.- Appendix B: Markovian Semigroups.- Appendix C: One-parameter semigroups of stochastic matrices.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Konrad Jacobs,K. Jacobs\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3764325917\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783764325916\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Birkhauser\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 02\/04\/2004\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 296\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.48lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.61h x 6.69w x 0.69d","brand":"Konrad Jacobs","offers":[{"title":"Hardcover","offer_id":48113856938239,"sku":"9783764325916","price":99.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_7c62a515-c0b2-4dca-b901-ca8de3b4c3a6.jpg?v=1769617598","url":"https:\/\/www.whiterainbookhouse.com\/products\/discrete-stochastics-konrad-jacobs-9783764325916","provider":"WR Book House","version":"1.0","type":"link"}