Applied Stochastic Processes

MATH 437 / MATH 535

Spring  ‘16

 

 

 

Course Logistics

Course Outline

Office Hours: Monday 3-4, Wednesday 2-3; 9-249 SSE Building

 

Exams

Exam I  

Exam II

 

Lectures

Lecture 1 - Introduction

Lecture 15 -Applications of DTMC IV

Lecture 2 - Probability Review I

Lecture 16 - Renewal Equation and Limit Theorems

Lecture 3 - Probability Review II

Lecture 17 - Birth and Death Processes

Lecture 4 - Probability Review III

Lecture 18 - Quasi Stationary Distribution

Lecture 5 - Probability Review IV

Lecture 19 - Branching Processes I

Lecture 6 - Discrete Time Markov Chains  I

Lecture 20 - Branching Processes II 

Lecture 7 - Discrete Time Markov Chains  II

Lecture 21 - Continuous Time Markov Chains

Lecture 8 - Discrete Time Markov Chains  III

Lecture 22 - Poisson Process & the Generator Matrix

Lecture 9 - Discrete Time Markov Chains  IV

Lecture 23 - The Embedded Chain & Kolmogorov Equations

Lecture 10 - Discrete Time Markov Chains  V

Lecture 24 - Kolmogorov Equations & Limit Theorems

Lecture 11 -Discrete Time Markov Chains VI

Lecture 25 - PDE for the Generating Function

Lecture 12 - Applications of DTMC I

Lecture 26 - Applications of CTMC

Lecture 13 -Applications of DTMC II

Lecture 27 - Statistical Inference for Markov Chains I

Lecture 14 -Applications of DTMC III

Lecture 28 - Statistical Inference for Markov Chains II

 

Readings

Epithelial Cell Division : Gibson et.al

 

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

 

Modeling Peer Pressure using DTMC : Cohen

 

Persistence Time in Stochastic Population Models : Allen et al.

 

Estimating Transition Matrix of a Homogenous Markov Chain : Craig and Sendi

 

 

 

Homework Assignments

 

Homework 1: Due 15/02/2016

 

Homework 2: Due 07/03/2016

 

Homework 3: Due 28/03/2016

 

Homework 4: Due 25/04/2016

 

 

MATLAB’ Stuff

Uniform

Poisson

Normal

Binomial

Exponential

Bi-Variate Normal

Snakes & Ladders (Matrix Method)

(CODE by Waleed)

Snakes & Ladders (Monte Carlo)

(CODE by Waleed)

MCMC Normal 1-D

(CODE by Beesham)