I am not sure yet.
Some kind of alternative extension of integrals which happens to make pathwise calculations ove stochastic integrals simple, in some sense.
I am pretty sure they mean *rough* in the sense of *approximate* rather than the sense of *not smooth*.
Or maybe both?

Seems to originate in a fairly impenetrable body of work by Lyons, e.g. T. Lyons (1994) but modern recommendations are to read Friz and Hairer (2020), available free online, as an introduction, which covers the simplest (?) case of Gaussian noise.

### Discrete approximations

Wong-Zakai approximations Twardowska (1996). (Martin Hairer recommendation.)

Possibly compact refs: (Kelly 2016; Kelly and Melbourne 2014).

### In learning

Hodgkinson, Roosta, and Mahoney (2021) makes use of rough path integrals to justify learning by the adjoint method in stochastic differential equations.

## Signatures

Chevyrev and Kormilitzin (2016) discusses path signatures in particular, which is something arising in the theory about which I know little.

## Code

## References

*Advances in Neural Information Processing Systems*. Vol. 32. Curran Associates, Inc.

*arXiv:1603.03788 [Cs, Stat]*, March.

*A Course on Rough Paths*. Edited by Peter K. Friz and Martin Hairer. Universitext. Cham: Springer International Publishing.

*Uncertainty in Artificial Intelligence*37 (July): 11.

*SIAM Journal on Financial Mathematics*11 (2): 470β93.

*The Annals of Applied Probability*26 (1).

*Mathematical Research Letters*1 (4): 451β64.

*arXiv:1405.4537 [Math, q-Fin, Stat]*, May.

*Proceedings of the 4th International Symposium on Information and Communication Technologies*, 223β28. WISICT β05. Cape Town, South Africa: Trinity College Dublin.

*Acta Applicandae Mathematica*43 (3): 317β59.

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