This question was posted in https://math.stackexchange.com but I got hardly any view. If posting here is an objection please let me know I would delete it immediately.
This question has evolved from watching the video: https://www.youtube.com/watch?v=dh5hHpJ79jc
In the video the speaker talked about white noise case and $\alpha$ related to the Holder condition, (wikipedia link to Holder condition https://en.wikipedia.org/wiki/H%C3%B6lder_condition)
The question: Is there a relation between SNR (https://en.wikipedia.org/wiki/Signal-to-noise_ratio) and Holder condition?
Let me be more specific, As I understand, Rough path theory (https://en.wikipedia.org/wiki/Rough_path) is related to the solution of differential equation driven by non-smooth signals and non-smoothness is defined in terms of Holder condition. In the video it clearly relates the white noise case to the value of $\alpha$. Consider our driver is simple sine wave, which is very smooth, but if we add a noise then we can define SNR of the driver based on the strength of the noise and at the same time can we define $\alpha$ based on the strength on the noise?
In some sense I am trying to define rough path theory in terms of SNR, is it possible? Any comments would be highly appreciated