Brownian motion of particles affects many branches of science. We report on the Brownian motion of micrometer-sized beads of glass held in air by an optical tweezer, over a wide range of pressures, and we measured the instantaneous velocity of a Brownian particle. Our results provide direct verification of the energy equipartition theorem for a Brownian particle. For short times, the ballistic ...

We present a decomposition of the sub-fractional Brownian motion into the sum of a fractional Brownian motion plus a stochastic process with absolutely continuous trajectories. The first application we show of this decomposition is the relation between the spaces of integrable functions with respect each one of these three processes. A general result of weak convergence to integrals of L(R) fun...

A family of reflected Brownian motions is used to construct Dyson’s process of non-colliding Brownian motions. A number of explicit formulae are given, including one for the distribution of a family of coalescing Brownian motions.