INTRODUCTION TO STOCHASTIC PROCESSES

Prerequisites & course information

Requisites: ( STAT/MATH 431 , 309 , STAT 311 , or MATH 531 ) and ( MATH 320 , 340 , 341 , 345 , 375 , 421 , or 531 ), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate) Course Designation: Core GenEd - Natural Science & Wellness Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties for stochastic processes (e.g., discrete space Markov chains, Poisson processes, renewal processes, branching processes, etc.). Audience: Both Grad & Undergrad 2. Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property (e.g., irreducibility, aperiodicity, recurrence, transience, the Markov property, etc.). Audience: Both Grad & Undergrad 3. Recall and state the standard theorems of stochastic processes. (e.g., laws of large numbers for Markov chains, existence of limiting/stationary distributions, law of large numbers for renewal processes, etc.) and recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Construct mathematical arguments related to the above definitions, properties, and theorems, including the construction of examples and counterexamples. Audience: Both Grad & Undergrad 5. Convey arguments in oral and written forms using English and appropriate mathematical terminology, notation and grammar. Audience: Both Grad & Undergrad 6. Model simple real life situations by means of discrete-space stochastic processes and calculate probabilities associated with those processes. Audience: Both Grad & Undergrad 7. Identify applications of course content in current areas of research. Audience: Graduate Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties for stochastic processes (e.g., discrete space Markov chains, Poisson processes, renewal processes, branching processes, etc.). Audience: Both Grad & Undergrad 2. Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property (e.g., irreducibility, aperiodicity, recurrence, transience, the Markov property, etc.). Audience: Both Grad & Undergrad 3. Recall and state the standard theorems of stochastic processes. (e.g., laws of large numbers for Markov chains, existence of limiting/stationary distributions, law of large numbers for renewal processes, etc.) and recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Construct mathematical arguments related to the above definitions, properties, and theorems, including the construction of examples and counterexamples. Audience: Both Grad & Undergrad 5. Convey arguments in oral and written forms using English and appropriate mathematical terminology, notation and grammar. Audience: Both Grad & Undergrad 6. Model simple real life situations by means of discrete-space stochastic processes and calculate probabilities associated with those processes. Audience: Both Grad & Undergrad 7. Identify applications of course content in current areas of research. Audience: Graduate