R. Srikant's Random Processes Notes, last taught Fall 2016
Preliminaries
The Probability Space
Independence and Conditional Probability
Random variables
Some Common RVs
Jointly Distributed RVs
Functions of RVs
Jensen, Markov, Chebyshev Inequalities
Chernoff Bound and CLT
Hoeffding Bound
Convergence of RVs
Law of Large Numbers
MMSE Estimation
MMSE Estimation for Random Vectors
Jointly Gaussian RVs
Random Walk
DTMCs
CTMCs
Other Random Processes
Random Process Examples
Martingales
Martingale Examples
Branching Processes
Stationarity, WSS and Ergodicity
Linear Systems
Power Spectral Density
The Sampling Theorem
Discrete-Time LTI Systems
Wiener Filter
Linear Innovations
Kalman Filter
Countable State-Space MCs
Foster-Lyapunov Theorem
Scheduling Algorithms
Gauss-Markov Processes
PCA and KL Expansion
EM Algorithm
References:
Hajek, Bruce. Random processes for engineers. Cambridge university press, 2015.
Gallager, Robert G. Stochastic processes: theory for applications. Cambridge University Press, 2013.
Grimmett, Geoffrey, and David Stirzaker. Probability and random processes. Oxford university press, 2020.