Brownian tree Brownian tree A Brownian tree, whose name is derived from Robert Brown via Brownian motion, is a form of computer art that was briefly popular in the 1990s, when home computers started to have sufficient power to simulate Brownian motion. Brownian trees are mathematical models of dendritic structures associated with the physical process known as diffusion-limited aggregation. A Brownian tree is built with these steps: first, a "seed" is placed somewhere on the screen. Then, a particle is placed in a random position of the screen, and moved randomly until it bumps against the seed. The particle is left there,
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