Increment definitions for scale dependent analysis of stochastic data

Matthias Waechter, Alexei Kouzmitchev, Joachim Peinke

It is common for scale-dependent analysis of stochastic data to use the increment $\Delta (t,r)=\xi (t+r)-\xi (t)$ of a data set $\xi (t)$ as a stochastic measure, where $r$ denotes the scale…