Stochastic Processes and Markov Chains

Explore practical probability, stochastic processes, and Markov chains through real-world modeling supported by MATLAB/Octave applications that reveal how randomness drives complex systems.

This course provides a practical introduction to probability, stochastic processes, and Markov chains, combining strong mathematical foundations with real-world problem solving supported by MATLAB applications.

It is designed for professionals seeking to strengthen analytical skills, students with no previous coursework in probability preparing for advanced quantitative study, and learners interested in applied stochastic modeling across fields such as finance, engineering, data science, and operations research.

Course Highlights: Foundations of Probability and Set Theory Discrete Random Variables and Probability Models Continuous Random Variables and Probability Distributions Joint Distributions and Pairs of Random Variables Random Vectors and Multivariate Probability Modeling Introduction to Stochastic Processes Discrete and Continuous-Time Markov Chains Practical MATLAB/Octave Applications integrated across all Probability, Stochastic Processes, and Markov Chains topics Course Benefits: Understand and apply foundational concepts in probability theory, including set theory and its relevance to probability.

Distinguish between discrete and continuous random variables and analyze their properties and applications.

Analyze pairs of random variables and random vectors, understanding their interactions within stochastic models.

Demonstrate proficiency in the basics of stochastic processes, with an emphasis on Markov chains and their theoretical and practical applications.

Use Markov chains to model and solve real-world problems across different fields using MATLAB to simulate stochastic processes and analyze data for practical insights.

Integrate stochastic modeling skills to support advanced data analysis and decision-making processes in professional or academic context Transferring for College Credit Credit earned in Extended Studies courses may lead to the award of a formal certificate by UC San Diego Division of Extended Studies or be applied toward an academic degree or professional credential, subject to at the approval of the receiving institution(s).

Course Typically Offered: Every quarter.

Exams will be given online during a set date and time.

Prerequisites: Before taking this course, students should have previously taken Calculus I , or an equivalent course.

Software: MATLAB/Octave - No prior experience or MATLAB/Octave license required for this course.

More information: For more information about this course contact unex-techdata@ucsd.edu .