To introduce students to a range of mathematical models that take account of the stochastic (random) fluctuations that are always present in the real world;
To demonstrate the circumstances in which continuous-time stochastic models give results that are different to those from deterministic models that neglect the random effects;
To provide a range of mathematical techniques and approximations that can be used to make analytic predictions from stochastic models;
Module learning outcomes
At the end of the module you should be able to...
appreciate the uses for stochastic models, their characteristics and limitations;
explain the concept of continuous-time stochastic processes and the Markov property;
give examples of applications of stochastic processes;
formulate and analyse Markov models in continuous time;
calculate (conditional) probabilities of events and expectations of variables described by simple Markov processes like the Poisson process or the Wiener process
determine transition rates and stationary distributions of birth-death processes
understand the basic properties of the Wiener process;
define the Ito stochastic integral and give its important properties.
Apply the Ito Lemma to verify if certain processes are martingales and to find solutions of certain stochastic differential equations;