25 March, at 4:30 pm, in room A 2.5 - Ricamo
Speaker: Helena Biščević
Title: Numerical modelling of stochastic differential equations
Abstract: The seminar will start with a gentle introduction to stochastic treatment of differential equations with the aim of making the audience comfortable with basic principles of stochastic analysis. We will try to clarify the difference in the approach between deterministic and stochastic differential equations (SDEs) and to which extent we can apply knowledge from the deterministic theory in order to treat SDEs. SDE assumes two functions in play, generating the behaviour of deterministic and stochastic part, often referred to as drift and diffusion coefficient, respectively. The importance of SDEs with non-Lipschitz coefficients will be motivated by examples from applications and naturally lead to open problems in the area.
For the rest of the talk, we will then introduce the basic methods used in numerical analysis for this type of equations. We will focus on some results on stability and contractivity of such equations through the lens of structure-preservation of numerical methods. If time permits, the results regarding preservation of invariant measure of SDEs by numerical methods will be presented.
Short bio: Helena Biščević is a Ph.D. student at Gran Sasso Science Institute.
Everybody is welcome.
