Arbitrary truncated Levy flight: Asymmetrical truncation and high-order correlations

► The generalized correlation approach is proposed to describe stochastic financial processes. ► High-order correlations of a non-Gaussian random walk with independent, identically distributed increments have been investigated. ► The cumulants of an asymmetrically truncated Levy distribution have been found. ► The behaviors of asymmetrically truncated Levy flight are considered.