Probability theory lecture notes pdf
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Conditional expectation 15-16 Martingales, Doob's decomposition Uniform integrability 17 Optional stopping, inequalities for Martingales 18-19 Convergence of Martingales 20-21 Convergence on metric spaces, Portmanteau theorem Lipschitz functions 22 Metrics for convergence of laws, empirical measures 23 Convergence and uniform tightness 24-25 Strassen's theorem, relationship between metrics 26-27 Kantorovich-Rubinstein theorem 28-29 Prekopa-Leindler inequality, entropy and concentration 30 Stochastic processes, Brownian motion 31 Donsker invariance principle 32-33 Empirical process and Kolmogorov's chaining 34-35 Markov property of Brownian motion, reflection principles 36 Laws of Brownian motion at stopping times Skorohod's imbedding 37 Laws of the iterated logarithm. Woods, Pearson Education, 3rd Edition. Statistical Theory of Communication — S. . Probability Methods of Signal and System Analysis.

Probability, Random Variables and Stochastic Processes — Athanasios Papoulis and S. First-Order Stationary Processes, Second- Order and Wide-Sense Stationarity, N-Order and Strict-Sense Stationarity, Time Averages and Ergodicity, Mean-Ergodic Processes, Correlation-Ergodic Processes, Autocorrelation Function and Its Properties, Cross-Correlation Function and Its Properties, Covariance and its properties, Linear system reponse of mean and mean squared value, Auto Correlation function, Cross Correlation Function, Gaussian Random Processes, Poisson Random Process. Follow us on and Support us with your Like. Probability and Random Processes with Application to Signal Processing — Henry Stark and John W. Spectral characteistics of system response: Power density spectrum of response, cross power spectral density of input and output of a linear system. Eugene Xavier, New Age Publications, 2003. .

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