Brownian noise to obtain the next one. A leaky integrator might be used in audio applications to ensure the signal does not "wander off". Note that while the first sample is random across the entire range that the sound sample can take on, the remaining offsets from there on are a tenth or there abouts, leaving room for the signal to bounce around. Brownian noise In science, Brownian noise (), also known as Brown noise or red noise, is the kind of signal noise produced by Brownian motion, hence its alternative name of random walk noise. The term "Brown noise" does not
Brownian excursion Brownian excursion process, formula_1, is a Wiener process (or Brownian motion) conditioned to be positive and to take the value 0 at time 1. Alternatively, it is a Brownian bridge process conditioned to be positive. Another representation of a Brownian excursion formula_1 in terms of a Brownian motion process "W" (due to Paul Lévy and noted by Kiyoshi Itō and Henry P. McKean, Jr.) is in terms of the last time formula_3 that "W" hits zero before time 1 and the first time formula_4 that Brownian motion formula_5 hits zero after time 1: Let formula_7 be the time that a