Probability distribution of the maximum of a smooth temporal signal

Clément Sire (1, 2)

1 PhyStat - Physique Statistique des Systèmes Complexes (LPT)
2 LPT - Laboratoire de Physique Théorique

We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal X(t). As an application, we compute the persistence exponent associated to the probability that the process remains below a non-zero level M. When X(t) is a Gaussian process, our results are expressed explicitly in terms of the two-time correlation function.

Mots clés: Persistence; random process; Gaussian walker; statistical process; Persistance; processus aléatoire; marcheur gaussien; statistique

Domaines: Autre [cond-mat.other]; Mécanique statistique [cond-mat.stat-mech]; Probabilités [math.PR]

Clément Sire. Probability distribution of the maximum of a smooth temporal signal. Physical Review Letters, 2007, 98, pp.020601. ⟨10.1103/PhysRevLett.98.020601⟩. ⟨hal-00079084⟩