Stochastic Processes

Course No.: SMI1131143     Credit(s):3

Course Description

Many systems evolve over time with an inherent amount of randomness. The purpose of this course is to develop and analyze probability models that capture the salient features of the system under study to predict the short and long term effects that this randomness will have on the systems under consideration. The study of probability models for stochastic processes involves a broad range of mathematical and computational tools. This course will strike a balance between the mathematics and the applications. The plan for the course is to cover: Conditional Probability and Conditional Expectation. Markov Chains in discrete time. Poisson Process. Markov Processes in continuous time. Martingale. Stationary Processes.

Course Learning Outcomes

On completion of the course, students should be able to:

lUnderstand and apply various topics in stochastic processes.

lThe “various topics” include conditioning and conditional probability, introductory theory of Markov chains (both discrete-time and continuous-time), Poisson and possibly other well-known stochastic processes.

Relationship to Other Courses

Pre-requisites: Linear Algebra, Calculus, Probability Theory and Mathematical Statistics

Textbook and Reading Lists

Textbook:

Bo Zhang, Hao Shang, Applied Stochastic Processes. China Renmin University Press, 2009.

Suggested reading lists:

Saeed Ghahramani, Fundamentals of Probability with Stochastic Processes (3rd edition). Prentice Hall, 2005.

Sheldon Ross, Introduction to Probability Models(10th edition). Academic Press, 2010.

Course Assessment

Course Schedule