Multi-scaling properties of truncated Levy flights

Abstract

Multi-scaling properties of one-dimensional truncated Levy flights are studied. Due to the broken self-similarity of the distribution of jumps, they are expected to possess multi-scaling properties in contrast to the ordinary Levy flights. We argue this fact based on a smoothly truncated Levy distribution, and derive the functional form of the scaling exponents. Specifically, they exhibit bi-fractal behavior, which is the simplest case of multi-scaling.

9 pages, 6 figures, accepted for publication in Phys. Lett. A

References in corpus (2)

• Universality in sandpiles
• Linear stochastic dynamics with nonlinear fractal properties

Cited by in corpus (25)

• Multifractal detrended fluctuation analysis of nonstationary time series
• Multifractal analysis of financial markets
• Wavelet versus Detrended Fluctuation Analysis of multifractal structures
• The components of empirical multifractality in financial returns
• Quantitative features of multifractal subtleties in time series
• Multifractality in the stock market: price increments versus waiting times
• Finite-size effect and the components of multifractality in financial volatility
• Components of multifractality in high-frequency stock returns
• Tempered Fractional Feynman-Kac Equation
• Effect of detrending on multifractal characteristics
• Multifractal characterization of gold market: a multifractal detrended fluctuation analysis
• Genuine multifractality in time series is due to temporal correlations
• Ergodic properties of continuous-time random walks: finite-size effects and ensemble dependences
• Photon trajectories in incoherent atomic radiation trapping as Levy flights
• Synthesis of scaling exponents: a fractional Levy model
• Area coverage of radial Levy flights with periodic boundary conditions
• Ultraslow Convergence to Ergodicity in Transient Subdiffusion
• Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses
• Radio-wave propagation in the non-Gaussian interstellar medium
• Disentangling sources of multifractality in time series
• Multifractality and its sources in the digital currency market
• Underdamped, anomalous kinetics in double-well potentials
• Corrupted bifractal features in finite uncorrelated power-law distributed data
• Quantifying patterns of punctuation in modern Chinese prose
• Random walks on bifractal networks