  Molecular simulations of many particles which move rather according to a
brownian than a newtonian type of dynamics, nevertheless, can be performed by
means of a "velocity-Verlet-like" algorithm. The derivation of this algorithm
requires the "Ito formula" of stochastic calculus which usually is not part of
a scientist's education. Therefore, it is going to be shown, how this formula
can be motivated and applied in order to find that algorithm. Furthermore, it
is demonstrated, why it is sufficient to use uniformly distributed random
numbers within that algorithm, thus avoiding gaussian distributed ones,
although gaussian distributed white noise forces are assumed to model the
brownian-like motion of the particles. Finally, a solution to the problem is
presented that the linear total momentum is not conserved due to the presence
of stochastic forces in the equations of motion of the particles.
