Many stochastic processes that you encounter are kind of well-behaved, i.e. have infinite variation, yet finite quadratic variation.

My question revolves around stochastic processes that have infinite variation, infinite quadratic variation but finite cubic variation. Of course you can go on like this for all degrees (like finite quartic variation, finite quintic variation etc.) up to infinity.

**My question**

Would you need one extra term with the respective degree for each step in new "Ito formulae"? Could you give an example of an Ito formula for a stochastic process that has infinite (quadratic) variation but finite cubic variation - or even a generalized Ito formula (is it comparable to a normal taylor series with infinitely many terms?)

*Full disclosure*

I originally asked this question on "MathUnderflow" nearly two months ago, yet have not received any answers.