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Stat171 Syllabus...

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Sta 171: Syllabus Natesh S Pillai [email protected] 1

What is this course about?

Stochastic processes collectively describe various random phenomena arising in nature and our daily life. We will study some important class of probabilistic models and deeply understand their properties. A recurring theme will be the use of stochastic processes for modeling in applied sciences. Computer simulations (in a language of your choice) will also play a major role in understanding the concepts. Use of the R language is encouraged, but not required. R syntax will not be tested in the course. Mostly, the course is mathematical at core. We will place key emphasis on concrete calculations for building intuition. Thus a solid background in Sta 110 (or equivalent course in solid undergraduate probability with solid footing on expectations, conditional expectations, familiarity with various distributions etc.) is a pre-requisite. Exposure to measure theoretic probability, though helpful, is not necessary to follow this course. If you don’t have the necessary background, please come talk with me.

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Logistics • Classroom: Science Center - E • Course time: Monday - Wednesday, 2:30-4:00. • Instructor: Natesh S. Pillai. Email: [email protected]. Email is the best way to reach me. Please be to sure have to the title STA 171 in your email to me. Office hours are Wednesdays 4-5. But if you have a quick question/clarification, please feel free to walk into my office any time. • Teaching Assistants: 1. John O’ Leary. Email: [email protected]. Section: TBA 2. Wenshuo Wang. Email: wenshuo [email protected]. Section: TBA 3. Hao Wu. Email: hao [email protected]. Section: TBA

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Textbooks

The only required text book is: Introduction to Stochastic processes with R, by Robert P. Dobrow. We will try to follow the chapters of Dobrow pretty closely, with some supplementary material. Students can download it for free from Harvard Library. Here is the link: http://onlinelibrary.wiley.com.ezp-prod1.hul.harvard.edu/book/10.1002/9781118740712; jsessionid=60034AEDB0AE23039906C072BEBAEE43.f04t04 Other useful books for reference include: 1. Introduction to Stochastic modeling, Fourth Edition. By Mark A. Pinsky and Samuel Karlin. Amazon link: http://www.amazon.com/Introduction-Stochastic-Modeling-Fourth-Edition/dp/ 0123814162 2. Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics), J.R. Norris. 3. Introduction to Stochastic Processes, Second Edition, Greg Lawler (Chapman & Hall/CRC Probability Series) 4. Probability with Martingales, David Williams, Cambridge University Press.

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Syllabus (tentative) • Jan 22-24: Motivation, Review of probability, Introduction to random walk and Brownian motion; Markov Chain First steps. (Chapters 1-2) • Jan 29-31: Markov chains long time behavior, Reversibility. (Chapter 3) • Feb 5-7: Branching Processes (Chapter 4) • Feb 12-14: Markov Chain Algorithms. Metropolis-Hastings, Gibbs Samplers. Coupling from the past. Cut-off (Chapter 5) • Feb 19-21: Feb 19 is presidents day. The First mid-term is on Feb 21. • Feb 26-28: Poisson process (Chapter 6) • March 5-7: Continuous time Markov chains, Birth-death Processes, Queues, Renewal processes (Chapter 7)

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• March 12-14: Spring Break • March 19-21: Martingales: introduction and examples, • March 26-28: The Second mid-term is on March 28. • April 2-4: Brownian motion. Introduction, Computations (Chapter 8) • April 9-11: Gaussian processes, Stochastic calculus (Chapter 9) • April 16-18: Stochastic Calculus, Ito’s formula (Chapter 9) • April 23-25: Review of Major Results; What next? (Chapter 9) • May ??: 2.5 hour Final, TBD.

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Grading

There will be weekly homework assignments. They will count for 20% of the final grade, the two mid-terms will each carry 20% weight, Final exam 35% and Class Participation will carry 5% weight. You are encouraged to collaborate with other students for homework problems, but you must write up your own solutions.

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