MATH 263: Stochastic Processes

San Jose State University, Spring 2021

Course information [syllabus]

Introductory course in stochastic processes and their applications. The course will cover discrete time Markov chains, the Poisson process, continuous time Markov processes, renewal theory, and Brownian motion.

Prerequisites: Math 39 and Math 163 (each with a grade of B or better)

Textbook: Introduction to Probability Models, Academic Press, 12th edition (March 9, 2019), by Sheldon M. Ross (Older editions of the book are fine for reading, but homework will be assigned based on the 12^th ed).

Technology and equipment requirements:

Canvas: Zoom recordings, assignments and grades will be posted in Canvas (accessible via http://one.sjsu.edu/).
Piazza: This course will use Piazza as the bulletin board. Please post all course-related questions there.
Equipment: Students should have access to a scanner (physical or cell phone app) in order to scan and submit their work.

Lecture slides

Slides are being continuously updated from Spring 2019. You are suggested to download a new copy right before each class (remember to refresh your browser).

Lectures		Textbook sections	Assignments
0	Course introduction and overview [slides] [syllabus]		Read Chapter 3 and Section 5.2
1	Probability review [slides]	3.2 - 3.5, 5.2	HW1
2	Markov chains [slides]	4.1, 4.2	HW2
3	Classification of states [slides]	4.3, 4.4a	HW3
4	Stationary distributions and limiting probabilities [slides]	4.4
5	Time reversible Markov chains [slides]	4.8	HW4
6	Mean time spent in transient states [slides]	4.6, 4.5.1	HW5
7	Branching processes [slides]	4.7
8	Poisson processes [slides]	5.3, 5.4	HW6
9	Continuous-time Markov chains [slides]	6.1 - 6.5	HW7
10	Brownian motion [slides]	10.1 - 10.3, 10.5	HW8
11	Gaussian processes (GP) [slides] GP regression [Stanford Lecture notes] [MATLAB Demo] [Book]	10.7
12	Spectral clustering [slides]	[A tutorial on spectral clustering] [NIPS paper] [NCut paper] [Diffusion maps paper]

Resources

Tables

Instructor feedback

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