Scale-invariant Truncated Lévy Process

Abstract

We develop a scale-invariant truncated Lévy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Lévy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the advantage that all moments are finite (and so accounts for the empirical scaling of the moments). To test the potential utility of the STL process, we analyze financial data.

4 pages, 6 figures; corrected typos; changed figure 3

References in corpus (2)

• The statistical properties of the volatility of price fluctuations
• Causal cascade in the stock market from the ``infrared'' to the ``ultraviolet''

Cited by in corpus (7)

• The footprint of atmospheric turbulence in power grid frequency measurements
• Record-breaking statistics for random walks in the presence of measurement error and noise
• On the scaling of the distribution of daily price fluctuations in Mexican financial market index
• Cumulant Approach of Arbitrary Truncated Levy Flight
• Monte Carlo-based tail exponent estimator
• Anomalous diffusion for a correlated process with long jumps
• Arbitrary Truncated Levy Flight: Asymmetrical Truncation and High-Order Correlations