28: Common Stochastic Processes

“Probabilities must be regarded as analogous to the measurement of physical magnitudes; that is to say, they can never be known exactly, but only within certain approximation.” – Emile Borel. “In its efforts to learn as much as possible about nature, modem physics has found that certain things can never be "known" with certainty. Much of our knowledge must always remain uncertain. The most we can know is in terms of probabilities” – Richard Feynman.

Lecture outline: Probability theory and Stochastic theory basics

1. Dependence in stochastic processes

Joint, conditional and marginal distributions

Stationarity

Dependence of stochastic processes

Memoryless dependence (Markov property) of stochastic processes

2. Common stochastic processes

Markov chains; Markov chains through an analogy

Characterizing a Markov Chain

Solving a Markov Chain

Types of stochastic processes: Birth death processes; Poisson process; Semi-Markov process; Random walk; Renewal Process.

Primary reference for this lecture:

“High Speed Networks and Internets: Performance and Quality of Service” by William Stallings; Chapter 7: “Overview of Probability and Stochastic Processes”

Secondary references for this lecture:

1. “Fundamentals of Performance Evaluation of Computer and Telecommunication System”, by Obaidat and Boudriga; Chapter 2: “Probability Theory Review”.

2. “Cartoon Guide to Statistics” by Larry Gonick; Chapter 3: “Probability” and Chapter 4: “Random Variables”.

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