Regular Conditional Distributions for Semimartingale SDEs

In this talk an existence result for the regular conditional distribution a large class of semi-martingale driven SDEs is presented. For this we show that the solution of these SDEs can be written as a measurable function of its driving processes into the space of all càdlàg functions equipped with the Borel algebra generated by all open sets with respect to the Skorohod metric. Our result is relevant, for example, in computational stochastics: as corollary it provides a Markov property which is essential for proving convergence results of numerical methods for general semi-martingale driven SDEs.

This is joint work with Michaela Szölgyenyi (University of Klagenfurt) and Paweł Przybyłowicz (AGH University of Science and Technology).