Lecture Instructor	Dr. Le Chen	lzc0090@auburn.edu
Class Meeting	TR, 12:30 PM -- 13:45 PM	Parker Hall 203
Office Hours	TR, 11:30 AM -- 12:20 PM

• When you send us emails, please do include the keyword Math 7820 or Math 7830 in the subject field of your email to ensure a timely response.
• In case you want to make an appointment with the instructor via Zoom, here is the link:
  https://auburn.zoom.us/j/8141875411

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This course forms the initial part of a two-course sequence focused on applied stochastic processes. In this introductory course, we will delve into both classical and contemporary aspects of stochastic processes. Topics under our purview, subject to course progress, will include Markov chain, Markov processes, renewal processes, Poisson processes, Random Walks, Martingales, and Brownian motion. Each of these areas will be examined in the context of their application to queues, population dynamics, statistic physics, and various other fields.

Our subsequent course (Math 7830) will further expand upon these foundational concepts, introducing stochastic integrals and stochastic differential equations, and examining their applications to mathematical finance, turbulence, polymers, and surface growth models, among others.

Our objective across these two courses is to equip students with a solid understanding and ability to apply stochastic processes in a multitude of real-world scenarios.

• Main textbook:
  • Karlin, Samuel; Taylor, Howard M.: A first course in stochastic processes. Second edition. Academic Press, New York-London, 1975. xvii+557 pp.
• Other references:
  • Billingsley, Patrick: Probability and measure. Third edition. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1995. xiv+593 pp.
• Comments: Both books are classical textbooks for stochastic processes and probability, which never go out of date. They are especially suitable for self studies. More references will be provided during the semester.
• More possible references:
  • Lawler, Gregory: Introduction to stochastic processes. 2nd edition. Chapman & Hall/CRC, Boca Raton, FL, 2006. xiv+234 pp.
  • Liao, Min: Applied stochastic processes. CRC Press, Boca Raton, FL, 2014. viii+199 pp.

Depending on the progress of the course, we will cover the following chapters of the textbook:

• Chapter 1. Elements of stochastic processes
• Chapter 2. Markov chains
• Chapter 3. The basic limit theorem of Markov chains and applications
• Chapter 4. Classical examples of continuous-time Markov chains
• Chapter 5. Renewal processes
• Chapter 6. Martingales
• Chapter 7. Brownian motion

Due to the small class size, we are able to provide a personalized teaching and learning experience. I encourage you to actively engage by bringing your personal goals, questions, and concerns to the forefront; we are committed to assisting you in achieving these objectives. The course format will primarily involve directed study, fostering collaborative discussions on the material and problem-solving. You are expected to diligently review the textbook and additional resources, and to engage deeply with the problem sets. To manage our course materials and assignments, we will utilize GitHub for version control. Essential technical skills such as using the Terminal with Tmux, the editor neovim, and the version control tool Git and GitHub will be taught and used as part of the curriculum. For your final assessment, you will embark on a project to create simulation tools and compile a comprehensive report, integrating the knowledge and skills acquired throughout the course.

The final grade in this course will be based on consistent performance and active participation throughout the semester. Our primary goals are to learn something interesting and useful, not only mathematics, and also technical aspects such as programming, version control, and writing. Therefore, I encourage you not to focus excessively on the final grades, but rather on the valuable learning experience and intellectual growth that this course offers.

• Simulations on Some Surface Growth Models
  1. GitHub
  2. Documentation

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• Students should familiarize themselves with Auburn honor code here
  • https://www.auburn.edu/academic/provost/academic-honesty/.
• Students are encouraged to share ideas and solutions on problem sets and labs, but must
  express those ideas in their own words in their submitted work.
• Students are not authorized to view or use the work of another student during exams.

Your success in this class is important to me. We will all need accommodations because we all learn differently. If there are aspects of this course that prevent you from learning or exclude you, please let me know as soon as possible. Together we will develop strategies to meet both your needs and the requirements of the course.

I encourage you to visit the Office of Accessibility to determine how you could improve your learning as well. You can register and make a request for services from the Office of Accessibility. In this case, please do inform me of such requests. See the following link for more information:

• https://accessibility.auburn.edu/

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