Stochastic Processes
Faculteit  Science and Engineering 
Jaar  2020/21 
Vakcode  WBMA04805 
Vaknaam  Stochastic Processes 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester II b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Stochastic Processes  
Leerdoelen  At the end of the course, the student is able to: 1) give an overview of the basic models used in modern probability theory and their interrelationships 2) prove the GaltonWatson theorem on the probability of extinction of a branching process 3) classify Markov chains according to properties such as recurrence/transience, irreducibility and periodicity. Can compute, using transition matrices, various quantities of interest pertaining to Markov chains, such as expected hitting times and exit probabilities. 4) compute quantities of interest for random walks on graphs using elementary potential theory. In particular, can prove Polya's theorem about recurrence and transience of random walks on lattices 5) prove some of the elementary properties of Brownian motion, such as continuity of trajectories and the distribution of the maximum of a trajectory. 6) derive basic theorems on points processes such as the superposition and thinning theorems 

Omschrijving  The aim of this course is to introduce several of the main stochastic processes that are being studied in modern probability theory and to showcase some attractive results. The course will cover: branching processes, random walks and Markov chains, Brownian motion, Poisson point processes, stochastic differential equations and percolation on lattices. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(final grade >= 5.5, Exam 70%, homework sets 30%) 

Vaksoort  bachelor  
Coördinator  prof. dr. T. Müller  
Docent(en)  prof. dr. T. Müller  
Verplichte literatuur 


Entreevoorwaarden  Prior knowledge assumed: Probability Theory, Linear algebra, Calculus 1&2, Analysis  
Opmerkingen  This course was registered last year with course code WBMA19013 

Opgenomen in 
