Numerical solution of stochastic differential equations
This course aims to provide an introduction to the numerical solution of stochastic differential equations. The presentation of the most used numerical techniques is equipped by the analysis of their most relevant properties in terms of accuracy, stability and conservation of invariance laws associated to the dynamics. The lectures also contain a substantive lab part (in MATLAB), helpful to confirm the theoretical properties and provide an experimental evidence of the effectiveness of the presented approaches.
Outline of the course: discretized Wiener process; simulation of stochastic integrals; one-step methods for SDEs: Euler–Maruyama and Milstein methods, stochastic theta-methods, stochastic Runge–Kutta methods; strong and weak convergence; linear stability analysis; nonlinear stability analysis; principles of stochastic geometric numerical integration.
Schedule:
Tuesday 15 November, 08:30–10:15;
Tuesday 15 November, 14:30–16:15;
Wednesday 16 November, 14:30–16:15;
Thursday 17 November, 10:30–12:15.
The course is offered by the PhD course in Mathematical and Physical Sciences of the University of Udine. Course page: https://www.dmif.uniud.it/dottorato/smf/offerta-didattica/numerical-solution-of-stochastic-differential-equations/.
Raffaele D’Ambrosio
Raffaele D’Ambrosio is full professor of Numerical Analysis at the University of L’Aquila. He got his Ph.D. in Mathematics in 2010, through a bi-nationally supervised program between the University of Salerno and Arizona State University. In 2011 he has been awarded with Galileo Galilei Prize for young researchers. In 2014, he has been Fulbright Research Scholar at Georgia Institute of Technology - School of Mathematics. In 2015 he achieved a researcher position at the University of Salerno and he became associate professor at the University of L’Aquila in 2017, where he covers the position of full professor since 2021. He is principal investigator of several granted national projects, author of more than 100 papers and member of the editorial board of international journals. His research interests range from structure-preserving numerical integration of deterministic and stochastic evolutive problems and the numerical approximation of deterministic and stochastic problems with memory to oscillatory problems and the diffusion of fake news. (http://people.disim.univaq.it/~raffaele.dambrosio/)
