Knowing the odds : an introduction to probability / John B. Walsh
- Author
- Walsh, John B.
- Published
- Providence, R.I. : American Mathematical Society, [2012]
- Copyright Date
- ©2012
- Physical Description
- xvi, 421 pages : illustrations ; 27 cm.
- Series
- Contents
- Machine generated contents note: ch. 1 Probability Spaces -- [§]1.1.Sets and Sigma-Fields -- [§]1.2.Elementary Properties of Probability Spaces -- [§]1.3.The Intuition -- [§]1.4.Conditional Probability -- [§]1.5.Independence -- [§]1.6.Counting: Permutations and Combinations -- [§]1.7.The Gambler's Ruin -- ch. 2 Random Variables -- [§]2.1.Random Variables and Distributions -- [§]2.2.Existence of Random Variables -- [§]2.3.Independence of Random Variables -- [§]2.4.Types of Distributions -- [§]2.5.Expectations I: Discrete Random Variables -- [§]2.6.Moments, Means and Variances -- [§]2.7.Mean, Median, and Mode -- [§]2.8.Special Discrete Distributions -- ch. 3 Expectations II: The General Case -- [§]3.1.From Discrete to Continuous -- [§]3.2.The Expectation as an Integral -- [§]3.3.Some Moment Inequalities -- [§]3.4.Convex Functions and Jensen's Inequality -- [§]3.5.Special Continuous Distributions -- [§]3.6.Joint Distributions and Joint Densities -- [§]3.7.Conditional Distributions, Densities, and Expectations -- ch. 4 Convergence -- [§]4.1.Convergence of Random Variables -- [§]4.2.Convergence Theorems for Expectations -- [§]4.3.Applications -- ch. 5 Laws of Large Numbers -- [§]5.1.The Weak and Strong Laws -- [§]5.2.Normal Numbers -- [§]5.3.Sequences of Random Variables: Existence* -- [§]5.4.Sigma Fields as Information -- [§]5.5.Another Look at Independence -- [§]5.6.Zero-one Laws -- ch. 6 Convergence in Distribution and the CLT -- [§]6.1.Characteristic Functions -- [§]6.2.Convergence in Distribution -- [§]6.3.Levy's Continuity Theorem -- [§]6.4.The Central Limit Theorem -- [§]6.5.Stable Laws* -- ch. 7 Markov Chains and Random Walks -- [§]7.1.Stochastic Processes -- [§]7.2.Markov Chains -- [§]7.3.Classification of States -- [§]7.4.Stopping Times -- [§]7.5.The Strong Markov Property -- [§]7.6.Recurrence and Transience -- [§]7.7.Equilibrium and the Ergodic Theorem for Markov Chains -- [§]7.8.Finite State Markov Chains -- [§]7.9.Branching Processes -- [§]7.10.The Poisson Process -- [§]7.11.Birth and Death Processes* -- ch. 8 Conditional Expectations -- [§]8.1.Conditional Expectations -- [§]8.2.Elementary Properties -- [§]8.3.Approximations and Projections -- ch. 9 Discrete-Parameter Martingales -- [§]9.1.Martingales -- [§]9.2.System Theorems -- [§]9.3.Convergence -- [§]9.4.Uniform Integrability -- [§]9.5.Applications -- [§]9.6.Financial Mathematics I: The Martingale Connection* -- ch. 10 Brownian Motion -- [§]10.1.Standard Brownian Motion -- [§]10.2.Stopping Times and the Strong Markov Property -- [§]10.3.The Zero Set of Brownian Motion -- [§]10.4.The Reflection Principle -- [§]10.5.Recurrence and Hitting Properties -- [§]10.6.Path Irregularity -- [§]10.7.The Brownian Infinitesimal Generator* -- [§]10.8.Related Processes -- [§]10.9.Higher Dimensional Brownian Motion -- [§]10.10.Financial Mathematics II: The Black-Scholes Model* -- [§]10.11.Skorokhod Embedding* -- [§]10.12.Levy's Construction of Brownian Motion* -- [§]10.13.The Ornstein-Uhlenbeck Process* -- [§]10.14.White Noise and the Wiener Integral* -- [§]10.15.Physical Brownian Motion* -- [§]10.16.What Brownian Motion Really Does.
- Subject(s)
- ISBN
- 0821885324 (alk. paper)
9780821885321 (alk. paper) - Bibliography Note
- Includes bibliographical references and index.
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