  The Doss-Sussmann (DS) approach is used for uniform simulation of the
Cox-Ingersoll-Ross (CIR) process. The DS formalism allows to express
trajectories of the CIR process through solutions of some ordinary differential
equation (ODE) depending on realizations of a Wiener process involved. By
simulating the first-passage times of the increments of the Wiener process to
the boundary of an interval and solving the ODE, we uniformly approximate the
trajectories of the CIR process. In this respect special attention is payed to
simulation of trajectories near zero. From a conceptual point of view the
proposed method gives a better quality of approximation (from a path-wise point
of view) than standard, or even exact simulation of the SDE at some discrete
time grid.

Probability