Rosa Preiß
Recalling the definition of branched rough paths, we demonstrate how it equivalently translates into the language of Martin Hairer's theory of regularity structures. Based on this example, we briefly introduce some basic concepts of the theory. While every individual branched rough path corresponds to a so-called model of the regularity structure, the concept of controlled rough paths is covered by the notion of controlled distributions for that model. Finally, the reconstruction theorem, which is the fundamental result of the theory, turns out to be trivial in our example.
