Parameter estimation for Rough Differential Equations

My goal is to estimate unknown parameters in the vector field of a rough differential equation, when the expected signature for the driving force is known and we estimate the expected signature of the response by Monte Carlo averages.

I will introduce the "expected signature matching estimator" which extends the moment matching estimator and I will prove its consistency and asymptomatic normality, under the assumption that the vector field is polynomial.  Finally, I will describe the polynomial system one needs to solve in order to compute this estimatior.