The Multifractal Model of Asset Returns is how, where the price of a financial asset is viewed as a multiscaling process with a long memory and long tails. According to Mandelbrot, “Fluctuations in “volatility” are introduced in the MMAR by a random trading time, generated as the c.d.f. of a random multifractal measure.” Trading time is the key concept facilitating the application of multifractals to financial markets. The notation is as follows:

X(t) = ln P(t) − ln P(0),

Where

1. X(t) is a compound process: X(t) ≡ BH[θ(t)] where BH(t) is a fractional Brownian Motion with self-affinity index H, and θ(t) is a stochastic trading time.
2. The trading time θ(t) is the c.d.f. of a multifractal measure defined on [0, T]. That is, θ(t) is a multifractal process with continuous, non-decreasing paths, and stationary increments.
3. {BH (t)} and {θ(t)} are independent.

It is detailed in this paper: https://users.math.yale.edu/~bbm3/web_pdfs/Cowles1164.pdf