Learning goals
The course provides a broad introduction to stochastic processes. In particular the aim is
- to give a rigorous introduction to the theory of stochastic processes,
- to discuss the most important stochastic processes in some depth with examples and applications,
- to give the flavour of more advanced work and applications,
- to apply these ideas to answer basic questions in several applied situations including biology, finance and search engine algorithms.

Knowledge and understanding
At the end of the course the students will be familiar with the basic concepts of the theory of stochastic processes in discrete and continuous time and will be able to apply various techniques to study stochastic models that appear in applications.

Applying knowledge and understanding
At the end of the course the students will have the tools to grasp and formalize, in the language of stochastic processes, phenomena that evolve in time and space. The students will have the tools to solve simple applied problems in new environments and broader contexts.

Making judgements
At the end of the course the students will have the tools to evaluate critically and choose between different stochastic models to model phenomena that evolve in time and space. The student will also acquire the necessary language skills to start reading academic books on the topic and research papers.

Communication skills
The students will acquire the intuition and the communication skills necessary to describe phenomena in the mathematical language of stochastic processes. In particular the student will also acquire the rationale behind the stochastic model studied (e.g. the ideas of Markovianity, transience, recurrence, equilibrium, stationarity, long and short-time behaviour...) that is necessary to communicate to specialist and non-specialist audiences.

Learning skills
The students will acquire the methodology and the language to study in a manner that may be largely autonomous and to apply the methodology to the subsequent studies in the area of statistics and finance.