Transcription of Stochastic Processes - Stanford University
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Stochastic Processes - Stanford University
Stochastic ProcessesAmir Dembo (revised by Kevin Ross)August 21, 2013E-mail of Statistics, Stanford University , Stanford ,CA 1. Probability, measure and Probability spaces and random variables and their Convergence of random Independence, weak convergence and uniform integrability25 Chapter 2. Conditional expectation and Hilbert Conditional expectation: existence and Hilbert Properties of the conditional Regular conditional probability46 Chapter 3. Stochastic Processes : general Definition, distribution and Characteristic functions, Gaussian variables and Sample path continuity62 Chapter 4. Martingales and stopping Discrete time martingales and Continuous time martingales and right continuous Stopping times and the optional stopping Martingale representations and Martingale convergence Branching Processes : extinction probabilities90 Chapter 5.
1.1. Probability spaces and σ-fields 7 1.2. Random variables and their expectation 11 1.3. Convergence of random variables 19 1.4. Independence, weak convergence and uniform integrability 25 Chapter 2. Conditional expectation and Hilbert spaces 35 2.1. Conditional expectation: existence and uniqueness 35 2.2. Hilbert spaces 39 2.3.
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