Description

Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time-varying randomness. Despite being listed as a seminar, this course is intended as an introduction to probability and stochastic processes for graduate students primarily interested in applications. If you plan to take only one probability course in your graduate studies, this course is meant for you. It may also serve as a complement to a more rigorous course. Unlike the measure-theory-based MATH 275 sequence, this course will emphasize modeling, analysis and simulation of applied stochastic processes as opposed to rigorous proofs (although there will be some proofs). Time permitting, a range of applications from biology to economics will be discussed. No background in probability will be assumed, but the pace will be quite fast and an undergraduate course in probability will be an asset. Here is a tentative list of topics to be covered:

• Overview of Basic Probability: Events; Random variables; Generating functions; Basic limit laws; Simulation.
• Introduction to Stochastic (mostly Markov) Processes: Poisson processes; Branching processes; Markov chains and continuous-time Markov processes; Diffusion processes and numerical methods (if time permits).

General Information

• Instructor: Sebastien Roch. To communicate with me, use Piazza.
• Time and place: MWF at 2 in MS 5147
• Office hours: TBA
• Prerequisites: No probability background is required. An undergraduate course in probability and stochastic processes (e.g. MATH 170) will be useful.
• Texts (not required): Topics covered will be taken mostly from
  • Probability and Random Processes by Grimmett and Stirzaker
  • Markov Processes and Applications: Algorithms, Networks, Genome and Finance by Pardoux
  • Applied Probability by Lange (available to UCLA students for free on the Springer website)
  • Adventures in Stochastic Processes by Resnick
• Grades will be based on a few homework assignments which may involve simulation.
• Piazza: We will use Piazza, a free discussion board. You should sign up here with your UCLA email by looking up the class. On Piazza, you can:
  • Ask course-related questions
  • Collaborate to form a high-quality Wikipedia-style response
  • Have a traditional thread-style discussion
  • Customize how Piazza notifies you of new posts (e.g., in real time, in daily digests, etc.)
  • Posts can be anonymous if you wish.
  You are strongly encouraged to post any questions about course content or policies here, and to help answer your fellow students questions. There are things to be kept in mind while using Piazza. Here are the rules:
  • Do not post solutions to the assignments, although feel free to discuss the problems without giving away too much.
  • Be civilized; refrain from posting offensive, inappropriate, or irrelevant content. Remember that the whole class, including the professor and the TAs, are potentital readers to the discussion board. Use your common sense to determine what constitutes as acceptable content.
  If you have questions for me of a more personal nature, use a private post. I will also post course announcements there, so it is important to check it regularly.

News

• [Mar 30]: Please take the poll on Piazza. It is completely anonymous and it will help me prepare the class.
• [Mar 30]: All future announcements, including homework assignments, will be posted on Piazza.