Non-parametric estimation of a Langevin model driven by correlated noise

Langevin models are widely used to model various stochastic processes in different fields of natural and social sciences. They adapted measured data by estimation techniques such as maximum likelihood estimation, Markov chain Monte Carlo methods, or the non-parametric direct method introduced Friedrich et al. (Phys Lett A 271(3):217, 2000). The latter has distinction being very effective context large sets. Due their $$\delta $$ -correlated noise, standard limited Markovian dynamics. non-Markovian can be formulated introducing a hidden component that realizes correlated noise. For partially observed diffusion version was Lehle Rev E 97(1):012113, 2018). However, this procedure requests correlation length noise is small compared component. In work, we propose without restriction. This allows one effectively deal with sets from wide range examples. We discuss abilities proposed using several synthetic