Probability Models (L7) (973G1)
15 credits, Level 7 (Masters)
Autumn teaching
This is the first optional Probability module, where we begin to study stochastic (random) processes. In this module our processes are in discrete time, so a stochastic process is a sequence of random variables where we can view it as a (discrete) time evolution of a random experiment. Stochastic processes are used to model several phenomena with uncertain outcomes, such as stock values, the weather, or the profit evolution of a gambler as they evolve through time.
You will develop basic tools for the study of such processes in discrete time (which makes it less technical). The central objects of study are Markov chains and their various models. These include:
- branching processes
- finite Markov chains
- infinite countable Markov chains
- discrete martingales
- limits of sequences of independent random variables.
You will also develop your modelling skills. You will pay particular attention to questions such as:
- How can we model a certain problem using a discrete process?
- Can the model be used to estimate probabilities, expected values etc. If so, how?
- How can we understand what happens to the model when we look far into the future?