The Euler-Maruyama approximation for the absorption time of the CEV   diffusion
  A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV diffusion from the mathematical finance and show how a weakly consistent approximation for the absorption time can be constructed, using the Euler-Maruyama scheme. 
Pavel Chigansky and Fima C. Klebaner
math.PR cs.NA