Heavy-tail driven by memory

TL;DR

This paper introduces a novel stochastic process influenced by memory effects, capable of generating both exponential and heavy-tailed distributions, demonstrating that memory can be an alternative origin of heavy tails in stochastic systems.

Contribution

It analytically derives a new class of distributions from a memory-driven process and shows how memory effects can produce heavy-tail behavior, supported by both analytical and numerical results.

Findings

Distribution derived from the process converges analytically.

Memory effects can generate power-law decay behavior.

Numerical investigations support the analytical results.

Abstract

We propose a stochastic process driven by memory effect with novel distributions including both exponential and leptokurtic heavy-tailed distributions. A class of distribution is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation and the closed form moment generating function is obtained, thus the cumulants are calculated and shown to be convergent. The other class of distributions are numerically investigated. The concoction of the two stochastic processes of the different signs of memory under regime switching mechanism does incarnate power-law decay behavior, which strongly implies that memory is the alternative origin of heavy-tail.