SE 377. Stochastic Processes and Applications
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Classification of stochastic Processes.
Convergence of random variables- in probability, almost sure, in weak topology, in norm, complete convergence and r-quick convergence, rate of convergence.
Martingales- convergence theorems.
Markov Property, asymptotic stationarity, ergodicity.
Wiener process and stochastic (Ito) intergral
Ergodic hypothesis, Measure preserving transformations, Poincare's recurrence theorem, ergodic theorem, mixing conditions.
Applications to sequential analysis, change detection problem, signal detection, source and channel coding, control problem, queueing networks and statistical physics.
References
- Robert Ash and M.F. Gardner (1975), Topics in Stochastic Processes, Academic Press.
- John Lamperti (1977) Stochastic Processes- A Survey of Mathematical Theory, Springer.
- L. Breiman (1992) Probability, Society for Industrial and Applied Mathematics (available in paperback) or 1968 (first) edition by Addision Wesley.
- P. Walters (2000), An Introduction to ergodic Theory, Springer, available in paperback or 1982 first edition by Springer.
- P. Billingsley (1967), Convergence of Probability Measures, Wiley.
- Selected issues of Annals of Probability and IEEE Transactions on Information Theory.
- Prerequisite-
- An Exposure to probability through courses such as ESO 209 or of higher level. Exposure to analysis/ measure theory is of additional help.
- Desirable background:
- Exposure to communication theory or mathematical analysis or advanced probability theory.
- Proposed by:
- Dr. R.K. Bansal, Department of Electrical Engg.
- Of Interest to:
- B.Tech. (CS, CE, Ch.E, A.E., E.E) Msc. (Maths, Statistics, Physics)
- Semester:
- Even
- Eligibility:
- Fourth year students