Applied Stochastic Processes

MATH 437 / MATH 535

Spring 22

 

Course Logistics

 

Course Outline

Office Hours: Thurs-Fri - 1:00-2:00

TA(s): Ayesha Ahmed (18070007@lums.edu.pk)

TA Office Hours: TBA

 

Lectures

 

Lecture 1 - Introduction	Lecture 14 - Applications of DTMC II Random Walk with Absorbing Boundaries I
Lecture 2 - Review of Probability I Video Lecture Class Notes	Lecture 15 - Applications of DTMC III Random Walk with Absorbing Boundaries II
Lecture 3 - Review of Probability II	Lecture 16 - Applications of DTMC IV Semi Infinite Random Walk
Lecture 4 - Review of Probability III	Lecture 17* - Birth & Death Processes (Extra Lecture)
Lecture 5 - Simulating Random Variables	Lecture 18 – Midterm Exam
Lecture 6 - Introduction to Discrete Time Markov Chains	Lecture 19 – Branching Processes I
Lecture 7 - Class Properties of a DTMC	Lecture 20 – Branching Processes II
Lecture 8 - Recurrence and Examples	Lecture 21 – Branching Processes III
Lecture 9 - Ergodicity	Lecture 22 – Continuous Time Markov Chains
Lecture 10 - Limit Theorems	Lecture 23 – Generator (Rate) Matrix
Lecture 11 - Stationary Distributions	Lecture 24 – Kolmogorov Equations
Lecture 12 - Mean First Passage and Absorption Times	Lecture 25 – Stationary Distribution
Lecture 13 - Applications of DTMC I: SIS Epidemic Model Video Lecture	Lecture 26* – Statistical Inference for Markov Chains (Extra Lecture)

 

Homework Sets

Homework 1 - Due in Class February 14, 2022

Homework 1: Solutions

Homework 2 - Due in Class March 02, 2022

Homework 2: Solutions

Homework 3 - Due in Class March 31, 2022

Homework 3: Solutions

Homework 4 - Due in Class April 25, 2022

Homework 4: Solutions

Homework 5 - Due in my Office May 12, 2022

 

 

 

Exams

 

Final - Due in my office May 17, 2022 (2 pm)

Midterm - Due in Class March 28, 2022

 

Readings & Interesting Links

 

The Magical Mind of Persi Diaconis: http://chronicle.com/article/The-Magical-Mind-of-Persi/129404/

The Search for Randomness (Video Lecture): https://www.youtube.com/watch?v=xit5LDwJVck

Counting of Urns and Balls: www.johndcook.com/TwelvefoldWay.pdf

Monsters that lurk on R: Constructing the Vitali Set, a set with �no size�

Modeling the Game of Snakes & Ladders: Schilling et.al

SIS Stochastic Model - Allen et.al.

A Markov Chain Model for Proliferating Epithelial Cells - Gibson et.al

A good resource for all things random: https://www.randomservices.org/random/index.html