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
Reflected Brownian motion all "t" ≥ 0, (with Φ the cumulative distribution function of the normal distribution) which yields (for "μ" < 0) when taking t → ∞ an exponential distribution For fixed "t", the distribution of "Z(t)" coincides with the distribution of the running maximum "M(t)" of the Brownian motion, But be aware that the distributions of the processes as a whole are very different. In particular, "M(t)" is increasing in "t", which is not the case for "Z(t)". The heat kernel for reflected Brownian motion at formula_9: formula_10 For the plane above formula_11 The stationary distribution of a reflected Brownian motion