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Accueil du site > Publications > Publications 2007 > Probability distribution of the maximum of a smooth temporal signal

Probability distribution of the maximum of a smooth temporal signal

Clément Sire

par Clément Sire - 5 juin 2006

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, f(t)=\langle X(0)X(t)\rangle.