Increment definitions for scale-dependent analysis of stochastic data.
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. For joint statistics of Delta(t,r) and Delta(t, r') the question of how to nest the increments on different scales r, r' is investigated. Here we show that in some cases spurious correlations between scales can be introduced by the common left-justified definition. The consequences for a Markov process are discussed. These spurious correlations can be avoided by an appropriate nesting of increments. We demonstrate this effect for different data sets and show how it can be detected and quantified. The problem allows to propose a unique method to distinguish between experimental data generated by a noiselike or a Langevin-like random-walk process, respectively.
Waechter
Matthias
M
Institute of Physics, Carl-von-Ossietzky University, D-26111 Oldenburg, Germany. matthias.waecheter@uni-oldenburg.de
Kouzmitchev
Alexei
A
Peinke
Joachim
J