Horatio Boedihardjo

The signature of a path

There has been a lot of activities recently pingrov path-wise results for stochastic differential equations. Some of these activities has been inspired by rough path theory which enables integration against the irregular sample paths to be defined in a path-wise, as opposed to L2, sense. While there have been many existence and uniqueness results, a natural next step is to develop descriptive path-wise theory for differential equations driven by specific path. In this talk, we study a particular example of differential equation and its solution, known as the signature. It is one of the simplest equations studied in rough path theory and has some interesting properties that general equations do not have.