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

Stochastic Covariant Derivatives in a (Curved) Space-Time: a Glimpse into the Fractoid Spaces