The theory of stochastic processes deals with phenomena evolving randomly in time and/or space, such as prices on financial markets, air temperature or wind velocity, spread of diseases, number of hospital admissions in certain area, and many others. This course introduces some of the basic ideas and tools to study such phenomena. In particular, we will introduce a concept of martingale to study phenomena evolving in discrete time and the concept of Poisson process (and its generalizations) and Brownian Motion to study processes evolving continuously in time. Some applications to statistical inference will also be discussed.

Pre-requisites: 24 units of level III mathematics or a degree in a numerate discipline or permission of the Head of Department.