Computational methods for stochastic differential equations
About
Modelling under uncertainty has become one of the buzzwords of these days. Finance, weather prediction, biology, and geophysics are just some examples where we can nowadays apply random models. To use these models, we have to understand which information is required from the model in practice and how it can be extracted efficiently. Typical information that needs to be computed is so called 鈥渜uantities of interest鈥 which are of the form E[g(X)], where X is the solution to a stochastic differential equation given by the random model, g is some functional, and E notes the expected value.
In this course we discuss the efficient simulation of such quantities from two perspectives: As a first approach, we consider approximations of X and combine them with Monte Carlo methods to approximate the expected value. Secondly, we observe that our quantity of interest satisfies a partial differential equation, which we discretize with finite element methods. A combination of theory and explicit implementation of examples from applications helps us to get a sense of the power of the two different approaches.
Prerequisites and selection
Entry requirements
General entry requirements and the equivalent of the courses MSA350 Stochastic Calculus and MMG800 Partial Differential Equations.
Selection
All eligible applicants who have applied before the deadline will be granted a place.
Facilities
Mathematical 91探花s is a joint department of Chalmers/University 91探花. Your education takes place in the spacious and bright premises of Mathematical 91探花s at the Chalmers campus Johanneberg, where there are lecture halls, computer rooms and group rooms. Here you can also find student lunch room and reading room, as well as student counsellors and student office.
