  In order to approximate the exit time of a one-dimensional diffusion process,
we propose an algorithm based on a random walk. Such an algorithm was already
introduced in both the Brownian context and in the Ornstein-Uhlenbeck context.
Here the aim is therefore to generalize this efficient numerical approach in
order to obtain an approximation of both the exit time and position for either
a general linear diffusion or a growth diffusion. The efficiency of the method
is described with particular care through theoretical results and numerical
examples.
