Probability distribution of the maximum of a smooth temporal signal.
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 with the probability that the process remains below a nonzero level M. When X(t) is a Gaussian process, our results are expressed explicitly in terms of the two-time correlation function, f(t)=X(0)X(t).
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Laboratoire de Physique Théorique, UMR 5152 du CNRS, Université Paul Sabatier, Toulouse Cedex 4, France.