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
The constant to be properly fixed to recover Schrödinger equation.
Marco Frasca (2012). Quantum mechanics is the square root of a stochastic process arXiv arXiv: 1201.5091v2