Asymptotic Behavior of Geometric Lévy α-Stable Flight

Ascertain the long-time asymptotic behavior and characterize the stationary-limit probability distribution, if any, for the geometric Lévy α-stable flight (GLF(α)) process, including whether a steady or quasi-steady state emerges in the long-time regime.

Background

The paper introduces and analyzes a new process—geometric Lévy α-stable flight (GLF(α))—and provides probability density solutions and simulations under threshold conditions. While the authors derive and validate finite-time behavior, they do not characterize the long-time regime or stationary limit for GLF(α).

The text explicitly states that the asymptotic behavior of this type of stochastic process remains an open question, motivating future investigation of steady or quasi-steady states and long-time distributional behavior.