Brownian motion of sol particles Brownian motion of sol particles Colloidal particles in a sol are continuously bombarded by the molecules of the dispersion medium on all sides. The impacts are however not equal in every direction. As a result, the sol particles show random or zig-zag movements. This random or zig-zag motion of the colloidal particles in a sol is called Brownian motion or Brownian movement. The phenomenon of Brownian motion was observed by Robert Brown in the form of random zig-zag motion of pollen grains suspended in water. This kind of movement is found in all colloidal systems. Such random motion is visible
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