  A study on the notion of covariant derivatives in flat and curved space-time
via It\^o-Wiener processes, when subjected to stochastic processes, is
presented. Going into details, there is an analysis of the following topics:
(i) Besov space, (ii) Schr\"odinger operators, (iii) Klein-Gordon and Dirac
equations, (iv) Dirac operator via Clifford connection, (v) semi-martingale and
Stratonovich integral, (vi) stochastic geodesics, (vii) white noise on a (4+)D
space-time $\mathfrak{H}$-geometry (with the Paley-Wiener integral), and (viii)
torsion of the covariant derivative. In the background stands the scale
relativity theory, together with a sketch of the concept of fractoid spaces.
