The Markov Switching Multi-fractal models as a new class of REM-like models in 1-dimensional space

Abstract

We map the Markov Switching Multi-fractal model (MSM) onto the Random Energy Model (REM). The MSM is, like the REM, an exactly solvable model in 1-d space with non-trivial correlation functions. According to our results, four different statistical physics phases are possible in random walks with multi-fractal behavior. We also introduce the continuous branching version of the model, calculate the moments and prove multiscaling behavior. Different phases have different multi-scaling properties.

References in corpus (1)

• Freezing and extreme value statistics in a Random Energy Model with logarithmically correlated potential

Cited by in corpus (2)

• Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations
• The calculation of multi-fractal properties of directed random walks on hierarchic trees with continuous branching