The module will introduce the basic ideas in modelling, solving and simulating stochastic processes.
Linked modules
Pre-requisites: MATH2011 OR ECON2041
Aims and Objectives
Learning Outcomes
Syllabus
Markov Chain
Definition and basic properties
Classification of states and decomposition of state space
The long term probability distribution of a Markov chain
Modelling using Markov chains
Time-homogeneous Markov jump process
Poisson process and its basic properties
Birth and death processes
Kolmogorov differential equations
Structure of a Markov jump process
Time-inhomogeneous Markov jump process
Definition and basics
A survival model
A sickness and death model
A marriage model
Sickness and death with duration dependence
Basic principles of stochastic modelling
Classification of stochastic modelling
Postulating, estimating and validating a model
Simulation of a stochastic model and its applications
Brownian motion: Definition and basic properties. Stochastic differential equations, the Ito integral and Ito formula. Diffusion and mean testing processes. Solution of the stochastic differential equation for the geometric Brownian motion and Ohrnstein-Uhlenbeck process
Learning and Teaching
Teaching and learning methods
Lectures, problem classes, coursework, surgeries and private study