Approximate Likelihood Construction for Rough Differential Equations
  The paper is split in two parts: in the first part, we construct the exact likelihood for a discretely observed rough differential equation, driven by a piecewise linear path. In the second part, we use this likelihood in order to construct an approximation of the likelihood for a discretely observed differential equation driven by a general class of rough paths. Finally, we study the behaviour of the approximate likelihood when the sampling frequency tends to infinity. 
Anastasia Papavasiliou and Kasia B. Taylor
math.ST stat.TH