分野別セミナー

In 2010, Fournier-Printems introduced a simple method for proving the existence of the density function of the time marginals of one-dimensional SDEs with linear growth coefficients. Debussche-Fournier (2013) and Romito (2018) extended this method to multi-dimensional case, and proved that the density function belongs to some Besov space. Their approach is based on "the one-step Euler scheme". On the other hand, Hutzenthalerm-Jentzen-Kloeden (2011) showed that if the coefficients of SDE grow super-linearly, then the standard Euler scheme does not converge to a solution of the equation. In order to approximate a solution of these SDEs, several "tamed Euler schemes" are proposed. In this talk, inspired by these previous research, we prove the Besov regularity of the density function for a class of SDEs with superlinearly growing coefficients. Our approach is based on "the one-step tamed Euler scheme". As an application of the regularity of the density function, we consider numerical analysis for irregular functionals of these SDEs.
This talk is based on joint work with Tsukasa Moritoki (Okayama university).