For its Winter 2026 term, the STOCHASTICA SNIP seminar will be held online every two weeks starting on October 14.  Talks of 30-45 minutes will be followed by 15-30 minutes of open discussion. Initially, seminars will be focused on introducing new problems and applications, to stimulate further discussions and ideas within individual working groups.  

This seminar is given by Mate Gerencser, TU Wien, and chaired by Charles-Edouard Brehier (leader of Working Group 5).

The doubly accelerated exponential Euler scheme for SPDEs

When approximating solutions of stochastic differential equations, a fundamental challenge is that the rate of convergence is often limited due to the low regularity of the solutions. When it comes to stochastic *partial* differential equations (SPDEs), this issue appears both in the time and space variable, limiting both temporal and spatial convergence rates. While the temporal rate has been significantly studied and in many cases successfully accelerated, no discretisation scheme of an SPDE has yet been able to achieve a spatial strong rate of convergence that is superior to the spatial regularity of the solution. We introduce a new numerical scheme that succeeds in overcoming this spatial order barrier. Numerical results confirm a substantial acceleration of the convergence speed. Joint work with Lukas Anzeletti and Helena Kremp.