A way to measure the complexity of random processes

Bongiorno Enea, Università del Piemonte Orientale
Chan Lax, Università del Piemonte Orientale
Goia Aldo, Università del Piemonte Orientale
Vieu Philippe, Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse, France

In this talk we consider the problem of measuring the complexity of a random process understood as the minimum number of independent random sources that characterize the process. This will be done by looking at the probability of small balls. In particular, we will assume that it factorizes in two terms: one dependent only on the center of the ball and the other dependent only on the radius. Since the second term contains the complexity information, this will be the main object of study and will be involved in the proposed inference methods. \\ The talk, based on recent works co-authored with L.Chan, A.Goia and P.Vieu, will be framed in a functional statistics setting.

Area: CS47 - Statistical inference in infinite-dimensional spaces (Alessia Caponera)

Keywords: small-ball probability; functional statistics; complexity

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