Entropy of Wiener integrals with respect to fractional Brownian motion

TL;DR

This paper investigates the complex entropy behavior of Wiener integrals with exponential functions concerning fractional Brownian motion, revealing intricate dependencies on time and Hurst index.

Contribution

It provides a detailed analysis of the entropy properties of exponent-Wiener-integrals with respect to fractional Brownian motion, highlighting their non-monotonic behavior.

Findings

Entropy of EWIFG-process varies with time and Hurst index

Unlike fractional Brownian motion, entropy exhibits complex, non-monotonic patterns

Detailed monotonicity properties are characterized in the paper

Abstract

The paper is devoted to the properties of the entropy of the exponent-Wiener-integral fractional Gaussian process (EWIFG-process), that is a Wiener integral of the exponent with respect to fractional Brownian motion. Unlike fractional Brownian motion, whose entropy has very simple monotonicity properties in Hurst index, the behavior of the entropy of EWIFG-process is much more involved and depends on the moment of time. We consider these properties of monotonicity in great detail.