Transcription of Probability Theory: STAT310/MATH230;August 27, 2013
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Probability Theory: STAT310/MATH230;August 27, 2013
Probability theory : stat310 / math230 ; August27, 2013 Amir DemboE-mail of Mathematics, Stanford University, Stanford, CA 1. Probability , measure and Probability spaces, measures and Random variables and their Integration and the (mathematical) Independence and product measures54 Chapter 2. Asymptotics: the law of large Weak laws of large The Borel-Cantelli Strong law of large numbers85 Chapter 3. Weak convergence,cltand Poisson The Central Limit Weak Characteristic Poisson approximation and the Poisson Random vectors and the multivariateclt141 Chapter 4. Conditional expectations and Conditional expectation: existence and Properties of the conditional The conditional expectation as an orthogonal Regular conditional Probability distributions171 Chapter 5. Discrete time martingales and stopping Definitions and closure Martingale representations and The convergence of The optional stopping Reversed MGs, likelihood ratios and branching processes212 Chapter 6.
7.3. Gaussian and stationary processes 286 Chapter 8. Continuous time martingales and Markov processes 291 8.1. Continuous time filtrations and stopping times 291 8.2. Continuous time martingales 296 8.3. Markov and Strong Markov processes 319 Chapter 9. The Brownian motion 343 9.1. Brownian transformations, hitting times and maxima 343 9.2.
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