Probability distribution of the maximum of a smooth temporal signal
Statistical Mechanics
2007-05-23 v2 Data Analysis, Statistics and Probability
Physics and Society
Abstract
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)=<X(0)X(t)>.
Keywords
Cite
@article{arxiv.cond-mat/0606145,
title = {Probability distribution of the maximum of a smooth temporal signal},
author = {Clément Sire},
journal= {arXiv preprint arXiv:cond-mat/0606145},
year = {2007}
}
Comments
Final version (1 major typo corrected; better introduction). Accepted in Phys. Rev. Lett