Short Description:
This course aims to introduce discrete (point) and continuous
stochastic processes. Required background is an undergraduate probability
course at the level of Bertsekas and Tsitsiklis. Familiarity with more
advanced concepts such as auto-correlation, power spectral density etc.
is not required, but can be useful.
Textbook: R.G. Gallager “Stochastic
Processes, Theory For Applications”, Cambridge Press 2013 (available
at bookstore).
Other texts:
1. R.G. Gallager, “Discrete Stochastic Processes,”
Kluwer Academic Press 1996. (This is the earlier lecture notes version
of the textbook.)
2. E. Çinlar, “Introduction to Stochastic Processes,”
Dover Publications, 2013, (reprinted version of 1975 version).
3. S.M. Ross, “Introduction to Probability Models,”
Academic Press, 2003.
4. D.P. Bertsekas and J.N. Tsitsiklis, “Introduction
to Probability,” Athena Scientific 2002.
5. A. Papoulis, “Probability, Random Variables, and
Stochastic Processes,” 3rd edition, McGraw Hill, 1991.
Course Outline:
1. (Chap.1) Probability Review, (probability space,
axioms, random variables, expectations, basic inequalities, stochastic
convergence, law of large numbers)
2. (Chap.2) Poisson Processes, (definitions, splitting-merging,
applications)
3. (Chap.3) Gaussian Processes, (Gaussian vectors,
covariance matrices, linear transformations, Gaussian processes, stationarity,
LTI filtering of Gaussian processes, power spectral density)
4. (Chap.4) Finite-state Markov Chains, (Classification
of states, matrix representation, ergodic chains, expected first passage
time, Markov decision theory)
5. (Chap.6) Countable-State Markov Chains, (steady-state,
positive recurrence, null recurrence)
6. (Chap.9) Random Walks, Threshold Crossings, Chernoff
Bound, Wald’s Inequality, Martingales.
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