It is well known that the Brownian motion and the related Wiener process have many different applications in different fields.

Roughly speaking, the Wiener process can be thought of as a function of two variables W(x, t).

Note that for each fixed x point W(x, t) = f(t) is a continuous function, often called a trajectory.

Various properties of such trajectories are known, one of them is that the function f(t) is not a function of finite variation in the Jordan sense, but f(t) is known to be a function of finite variation in Wiener sense, for some number p>1.

In the literature that I have access to, the connection between finite variation in the Wiener sense and Brownian motion ends with this last result.

I wonder what role the number p plays. Does the number p have any interpretation in physics, economics, or any other field?

I will be grateful if someone can refer to the literature that describes such interpretations of the number p.