  Brownian dynamics play a key role in understanding the diffusive transport of
micro particles in a bounded environment. In geometries containing confining
walls, physical laws determine the behavior of the random trajectories at the
boundaries. For impenetrable walls, imposing reflecting boundary conditions to
the Brownian particles leads to dynamics described by reflecting stochastic
differential equations. In practice, these stochastic differential equations as
well as their refinements are quite challenging to handle, and more
importantly, many physical processes are better modeled by processes
conditioned to stay in a prescribed bounded region. In the mathematical
literature, these processes are known as taboo processes, and despite their
simplicity, at least compared to the reflecting stochastic differential
equations approach, are surprisingly not much exploited in physics. This paper
explores some aspect of taboo processes and other constrained processes in
simple geometries: Interval in one dimension, circular annulus in two
dimensions, hollow sphere in three dimensions, and more. In particular, for the
two-dimensional taboo process in a circular annulus, the Gaussian behavior of
the stochastic angle is established.
