Course overview
This course introduces the fundamental concept of stochastic processes, particularly Markov chains, and related structures. These time-dependent probabilistic models are essential for modelling many real-world systems, be it a telecommunications network, a hospital waiting list or a transport system. They also arise in many other environments, where you wish to capture the development of some element of random behaviour over time, such as the state of a game or a decision process. Many advanced numerical methods in applied mathematics and machine learning are based on stochastic processes and this course will open up further study in these areas.
- Discrete time
- Continuous time
Course learning outcomes
- Explain the mathematical foundations of stochastic processes in both discrete and continuous time.
- Explain the short and long-term behaviour of Markov chains and how this relates to the properties of the underlying states.
- Apply the theory developed in the course for modelling and solving appropriate problems.
- Demonstrate skills in communicating mathematics.
- Write computer code to simulate different types of stochastic processes.
Degree list
The following degrees include this course