Levy de Castroet al.Reply:

Levy Statistics and Anomalous Transport: Levy Flights and Subdiffusion

III. Lévy flights 9 A. Underlying random walk process 9 B. Propagator and symmetries 10 C. Presence of external potentials 12 1. Harmonic potential 12 2. Steeper than harmonic potentials 13 D. First passage and first arrival of Lévy flights 15 E. Leapover properties of Lévy flights 17 F. Kramers problem for Lévy flights 18 G. More on the ”pathology” 20 H. Bi-fractional transport equations 22 I....

Levy model of cancer

Along an individual lifetime, stem cells replicate and suffer modifications in their DNA content. I model the modifications in the DNA of a single cell as a Levy flight, made up of small amplitude Brownian motions plus rare large-jumps events. The distribution function of mutations has a long tail, in which cancer events are located far away. The probability of cancer in a given tissue is rough...

Levy sections theorem revisited

This paper revisits Levy sections theorem, which generalizes the central limit theorem to encompass autocorrelated variables. Levy sections theorem’s approach is extended to time series and applied to historical daily returns of selected dollar exchange rates. We explain the elevated kurtosis usually observed in such series by their volatilities. In particular, the high kurtosis of emerging mar...

Levy and set theory

Azriel Levy (1934–) did fundamental work in set theory when it was transmuting into a modern, sophisticated field of mathematics, a formative period of over a decade straddling Cohen’s 1963 founding of forcing. The terms “Levy collapse”, “Levy hierarchy”, and “Levy absoluteness” will live on in set theory, and his technique of relative constructibility and connections established between forcin...

University of Groningen Levy walks evolve through interaction between movement and environmental complexity de Jager,