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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!

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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 $H>1/4$.

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  • $\begingroup$ Thanks for your response. I was thinking in a process driven by a non-Gaussian noise following the Tsallis q-Gaussian distribution. Approaches are generally made to transform the noise into a Markovian one, and I wanted to know if it is possible to use the theory of rough paths to be able to preserve the information regarding the non-Markovian part of the process. $\endgroup$
    – Roman22
    Feb 5, 2020 at 19:45

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