I would like to know whether there is a suitable extension of the theory of rough paths that could be useful to solve Non-Markovian problems. 


I would appreciate any example or also any other theory (not necessarily rough paths) that could give a formal framework to deal with non-Markovianity.


My main motivation is to solve 1D or 2D stochastic differential equations driven by non-Markovian processes, arising in physics (e.g., non-equilibrium thermodynamics).
Thanks!



Rough paths theory for Non-Markovian processes
It really depends on what sort of non-Markovian equations you have in mind, but it does certainly allow you to give solution theories for SDEs driven by fractional Brownian motion with Hurst parameter $H>1/4$.


