This paper is devoted to the estimation of the entropy of the dynamical system {Xα (t), t ≥ 0}, where the stochastic process Xα (t) consists of the fractional Riemann–Liouville integral of order α ∈ (0, 1) of a Gauss–Markov process. The study is based on a specific algorithm suitably devised in order to perform the simulation of sample paths of such processes and to evaluate the numerical approximation of the entropy. We focus on fractionally integrated Brownian motion and Ornstein–Uhlenbeck process due their main rule in the theory and application fields. Their entropy is specifically estimated by computing its approximation (ApEn). We investigate the relation between the value of α and the complexity degree; we show that the entropy of Xα (t) is a decreasing function of α ∈ (0, 1).
On the entropy of fractionally integrated gauss–markov processes
Pirozzi E.
2020
Abstract
This paper is devoted to the estimation of the entropy of the dynamical system {Xα (t), t ≥ 0}, where the stochastic process Xα (t) consists of the fractional Riemann–Liouville integral of order α ∈ (0, 1) of a Gauss–Markov process. The study is based on a specific algorithm suitably devised in order to perform the simulation of sample paths of such processes and to evaluate the numerical approximation of the entropy. We focus on fractionally integrated Brownian motion and Ornstein–Uhlenbeck process due their main rule in the theory and application fields. Their entropy is specifically estimated by computing its approximation (ApEn). We investigate the relation between the value of α and the complexity degree; we show that the entropy of Xα (t) is a decreasing function of α ∈ (0, 1).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
