forelesning

In the last weeks we discussed the existence and uniqueness of rough differential equations, a priori estimates of solutions and the continuity of the Ito-Lyons map (see Ch. 8 in the Friz, Hairer). As an application of those results, we studied the link between solutions of Ito-SDE´s and RDE´s. Further we obtained the Wong-Zakai theorem on the approximation of SDE-solutions by means of solutions to ODE´s (see Ch. 9). In our next lesson (4. May) we aim at proving the support theorem of Stroock-Varadhan, which provides a characterization of the support of the distribution of Ito-SDE-solutions (see Ch. 9). Another application of the above mentioned results, we want to look at in the next lesson, pertains to the construction of solutions to a certain class of rough path and stochastic partial differential equations (see Ch. 12). Our plan is to start with Ch. 13 on an introduction to regularity structures as a generalization of the theory of rough paths next week (11. May).