This paper studies an approximation method for the log likelihood function of a non-linear diffusion process using the bridge of the diffusion. The main result (Theorem 1) shows that this approximation converges uniformly to the unknown likelihood function and can therefore be used efficiently...

We extend Donsker's approximation of Brownian motion to fractional Brownian motion with Hurst exponent H∈(0,1) and to Volterra-like processes. Some of the most relevant consequences of our ‘rough Donsker (rDonsker) Theorem' are convergence results for discrete approximations of a large class...