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ECE 604

Stochastic Processes

Graduate

Fall 2025 · Stochastic Processing

Readings

  • Introduction to Probability Models
    Sheldon M. Ross · 12th · unspecified
    Academic Press, 2019.
  • Weihua Zhuang, ECE 604 Lecture Notes, available from W Print.
    unspecified
Fall 2024

Topics

  • Review of Probability: Distributions, Expectations, Conditioning, Bayes’ Theorem, Indepen- dence, Random Variables, Bounds: Markov, Chebychev, Chernov. Borel-Cantelli Lemmas.
  • Discrete-probability– counting arguments, branching processes.
  • Gaussian Random Variables, Conditioning, Conditional Expectation 1
  • Stochastic Processes : Classification: Gaussian, Poisson, Markov, structure of Gauss-Markov processes. Stationarity- Weak and strong laws. CLT, Convergence, Ergodic Theorems.
  • Wide sense stationary processes- L2- Theory of Stochastic Processes: AR and MA Approxi- mations. Wold decomposition and prediction of 2nd. order stationary processes. Bochner’s Theorem, Spectral Theory, Shannon sampling, Karhunen-Loeve Expansions.
  • Independent increment processes: Wiener process, Poisson Processes.
  • Discrete Markov chains: Classification, invariant distributions, ergodicity. Applications.

Readings

  • P. Bremaud, Probability Theory and Stochastic Processes, Universitext Series, Springer-Verlag, 2020 (This is an excellent and very recent book. My notes are very similar to the content of this
    unspecified
Fall 2023

Topics

  • Review: probability and conditional probability, random variables, probability density function, probability mass function, cumulative distribution function, mean and variance, moment generating functions.
  • Convergence concepts: convergence in mean square, convergence almost everywhere, convergence in probability, convergence in distribution.
  • Markov chains: Chapman-Kolmogorov equations, time reversibility, Markovian decision process.
  • Poisson processes: exponential distribution, Poisson process, generalization of the Poisson process.
  • Continuous-time Markov chains: birth and death process, transition probability function, time reversibility, uniformization.
  • Renewal processes: limit theorems, renewal reward process, regenerative process.
  • Stationary processes: Brownian motion, white noise, Gaussian process, stationary process.
  • for distribution (e.g. uploading material to a commercial third ‐party website) may lead to a violation of Copyright law.

Readings

  • Sheldon M. Ross, Introduction to Probability Models, 12nd ed., Academic Press, 2019 (Hardback ISBN: 9780128143469; eBook ISBN: 9780128143476)
    12nd ed. · unspecified
  • x Ian F. Blake, An introduction to applied probability, 1979 (call number: QA273.B586 1987)
    unspecified
  • x Sheldon M. Ross, A first course in probability, 9th ed., 2012 (ISBN10: 1-292-02492-5)
    9th ed. · unspecified
  • x Athanasios Papoulis, Probability, Random Variables, and Stochastic Processes, 2002 (QA273 .P2 2002)
    unspecified
Fall 2022

Topics

  • Review: probability and conditional probability, random variables, probability density function, probability mass function, cumulative distribution function, mean and variance, moment generating functions.
  • Convergence concepts: convergence in mean square, convergence almost everywhere, convergence in probability, convergence in distribution.
  • Markov chains: Chapman-Kolmogorov equations, time reversibility, Markovian decision process.
  • Poisson processes: exponential distribution, Poisson process, generalization of the Poisson process.
  • Continuous-time Markov chains: birth and death process, transition probability function, time reversibility, uniformization.
  • Renewal processes: limit theorems, renewal reward process, regenerative process.
  • Stationary processes: Brownian motion, white noise, Gaussian process, stationary process.

Readings

  • Sheldon M. Ross, Introduction to Probability Models, 11th ed., Academic Press, 2014
    11th ed. · unspecified
  • x Ian F. Blake, An introduction to applied probability, 1979 (call number: QA273.B586 1987)
    unspecified
  • x Sheldon M. Ross, A first course in probability, 9th ed., 2012 (ISBN10: 1-292-02492-5)
    9th ed. · unspecified
  • x Athanasios Papoulis, Probability, Random Variables, and Stochastic Processes, 2002 (QA273 .P2 2002)
    unspecified
Fall 2021

Topics

  • Review of Probability: Distributions, Expectations, Conditioning, Bayes’ Theorem, Indepen- dence, Random Variables, Bounds: Markov, Chebychev, Chernov. Borel-Cantelli Lemmas.
  • Discrete-probability– counting arguments, branching processes.
  • Gaussian Random Variables, Conditioning, Conditional Expectation 1
  • Stochastic Processes : Classification: Gaussian, Poisson, Markov, structure of Gauss-Markov processes. Stationarity- Weak and strong laws. CLT, Convergence, Ergodic Theorems.
  • Wide sense stationary processes- L2- Theory of Stochastic Processes: Bochner’s Theorem, Spectral Theory, Shannon sampling, Karhunen-Loeve Expansions. AR and MA Approxima- tions. Wold decomposition and prediction of 2nd. order stationary processes.
  • Independent increment processes: Wiener process, Poisson Processes.
  • Introduction to Markov chains: Classification, invariant distributions, ergodicity.
  • Introduction to martingales. The two pillars of martingale theory: Optional sampling and martingale convergence.
  • Additional remarks
  • All exams will be open notes.
  • Students are advised to be regular and attempt to solve the problem sets on their own.
  • Dishonesty will be dealt with harshly according to the rules of the university. 3

Readings

  • P. Bremaud, Probability Theory and Stochastic Processes, Springer-Verlag, 2020. This is an excellent book. My notes closely follow the exposition in this book in terms of
    unspecified
Fall 2020

Readings

  • Sheldon M. Ross, Introduction to Probability Models, 11th ed., Academic Press, 2014
    11th ed. · unspecified
  • for Chapters 1-3 (reserved in DC library):  Ian F. Blake, An introduction to applied probability, 1979 (call number: QA273.B586 1987)  Sheldon M. Ross, A first course in probability, 9th ed., 2012 (ISBN10: 1-292-02492-5)  Athanasios Papoulis, Probability, Random Variables, and Stochastic Processes, 2002 (QA273 .P2 2002)
    9th ed. · unspecified
Fall 2017

Readings

  • S. M. Ross: Introduction to Probability Models, 4th Edition, Academic Press, 1989 (good for refreshing probability but lacks wide sense theory)
    4th Edition · unspecified
  • G. Grimmett and D. R. Stirzaker: Probability and random Processes, 3rd. Edition, Cambridge University Press, 2002. (excellent book but a bit advanced and not enough on wide-sense theory)
    unspecified
Sources