Title: Learning and forecasting of irregular dynamics
Abstract: Let us consider an evolution equation dY(t)= A(X).dX(t) of a scalar quantity Y controlled by an irregular (non-differentiable, of infinite variation) vector trajectory X. What can we say about the control A(.) from the observation of the trajectories of Y and X?
This type of problem arises, for example, in the supervision and control of risks in financial portfolios whose exact composition is unknown but whose value is observed, or also in other control and regulation problems in systems subject to irregular evolution.
We present an algorithm for classifying controls A(.) from (discrete) observations of Y and X.
Our approach uses the concept of signing an irregular trajectory, due to Chen (1958) and developed by T Lyons, which we combine with a ‘machine learning’ approach to obtain an algorithm that can be deployed on multidimensional data streams.
