Class Notes

 

DRAFT OF  STOCHASTIC PROCESSES: THEORY FOR APPLICATIONS (5/4/2012)

This is a preliminary draft of a forthcoming book. It revises and extends `Discrete

Stochastic Processes' (1996). It also adds chapters on Gaussian processes,

detection, hypothesis testing, and estimation

1. Table of contents, introduction, and review of probability
2. Poisson processes
3. Gaussian random vectors and processes
4. Finite-state Markov chains
5. Renewal processes
6. Countable-state Markov chains
7. Markov processes with countable state spaces
8. Detection, decisions, and hypothesis testing
9. Random walks, large deviations, martingales
10. Estimation and bibliography

NOTES ON INFORMATION THEORY

These notes were written for an information theory course at MIT in 1992

but are not edited carefully.

1. Variable to Fixed Length Source Coding - Tunstall Codes (1992)
2. Variable to Fixed Length Adaptive Source Coding - Lempel-Ziv Coding (1992)
3. Lempel-Ziv Sliding Window Universal Compression (Revised 1994)
4. Arithmetic Coding (1992)
5. The Arimoto Blahut Algorithm for finding Channel Capacity (revised 1994)
6. Fixed Composition Arguments and Lower Bounds to Error Probability (1992)
7. A Random Coding Bound on Fixed Composition Codes (1992)
8. Galois Fields (1992)
   

 

NOTES ON RANDOM PROCESSES

These earlier notes have been revised and edited and are now included in the

draft of Stochastic processes: theory for applications above.