Markov process built in scale-similar multifractal energy cascades in turbulence

The scale-similar multifractal cascade, which is believed to describe the process of energy cascade in the inertial scale-range of isotropic turbulence, is proved to be Markovian so as to be governed by the Chapman-Kolmogorov equation, when negative logarithmic length scale is taken for time. For a limited class of cascades, the Kramers-Moyal expansion of the Chapman-Kolmogorov equation is possible and the coefficients are exactly derived from the functional form of intermittency exponents mu(q), and they are all constant if the cascade is scale similar.