After having fixed the definition of the extended Itō integral, I have posted a revised version of my paper on arXiv (see here). The idea has been described here. A full account of this story is given here. The interesting aspect from a physical standpoint is the space that is fluctuating both for a Wiener process and a Bernoulli process, the latter representing simply the tossing of a coin. We can sum up everything in the very simple formula
![dX(t)=[dW(t)+\beta dt]^\frac{1}{2}.](https://s0.wp.com/latex.php?latex=dX%28t%29%3D%5BdW%28t%29%2B%5Cbeta+dt%5D%5E%5Cfrac%7B1%7D%7B2%7D.&bg=ffffff&fg=333333&s=0&c=20201002)
The constant 
Marco Frasca (2012). Quantum mechanics is the square root of a stochastic process arXiv arXiv: 1201.5091v2
The Gauge Connection 
[…] Further update: I have posted a revised version of the paper with a proper definition of this generalized class of Ito integrals (see here). […]