F70SP - Stochastic Networks

Course leader(s):

Aims

To introduce stochastic processes used in stochastic and statistical modelling , and to provide an introduction to modern mathematical tools for study such processes

Syllabus

1. Probabilistic Methods (1.1 - Compound distributions, 1.2 - Sums of indicator random variables, 1.3 - Coupling, 1.4 - Stochastic dominance, 1.5 - Probabilistic bounds)

2. Branching processes (2.1 - BPs in discrete time, 2.2 - BPs in continuous time)

3. Models of random graphs (3.1 - Erdos-Renyi graph, 3.2 - Generalised random graph, 3.3 - Configuration model, preferential attachment model)

Learning outcomes

By the end of the course, students should be able to do the following:

Apply approximation techniques to sums of indicator random variables
Apply probability bounds to sums of random variables
Explain friendship paradox via size-biased distributions
Define a branching process
Explain why the number of individuals in a branching process grows exponentially
Define Erdos-Renyi random graphs and generalised random graphs
Calculate numerical characteristics of numbers of subgraphs of interest in random graphs

Further details

Curriculum explorer: Click here

SCQF Level: 10

Credits: 15