| Abstract: |
| This talk presents recent advances in the numerical preservation of qualitative and quantitative features in stochastic ordinary and partial differential equations, with focus on two main directions.
The first concerns the geometric integration of stochastic Hamiltonian systems. Two different settings are considered: in the Ito case, the expected Hamiltonian typically displays a linear drift in time, while in the Stratonovich case the Hamiltonian is preserved pathwise. The talk discusses how suitable numerical methods reproduce these behaviors and addresses their long-time properties through backward error analysis.
The second direction regards structure-preserving discretizations for dissipative stochastic problems. In this context, the focus is on the preservation of mean-square contractivity under time discretization, especially for stochastic theta-methods. The analysis shows that such contractivity can be retained under appropriate stepsize restrictions. A unifying perspective throughout the talk is the existence of a bridge between the numerical treatment of stochastic problems and the corresponding deterministic theory.
This presentation is based on joint work with Helena Biscevic (Gran Sasso Science Institute), Chuchu Chen (Chinese Academy of Sciences), David Cohen (Chalmers University of Technology & University of Gothenburg), Stefano Di Giovacchino (University of L`Aquila), and Annika Lang (Chalmers University of Technology & University of Gothenburg). |
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