  We prove a theorem showing that quantum mechanics is not directly a
stochastic process characterizing Brownian motion but rather its square root.
This implies that a complex-valued stochastic process is involved.
Schr\"odinger equation is immediately derived without further assumptions using
It\=o integrals that are properly generalized. Fluctuations in space arise from
a Brownian motion and the combined effect of a stochastic process with a
symmetric Bernoulli distribution typical of tossing a coin.
