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 the Ornstein–Uhlenbeck context, that is for particular time-homogeneous diffusion processes. 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 a general linear diffusion. The main challenge of such a generalization is to handle with time-inhomogeneous diffusions. The efficiency of the method is described with particular care through theoretical results and numerical examples.

为了近似一维扩散过程的退出时间，我们提出了一种基于随机游走的算法。已经在布朗上下文和Ornstein-Uhlenbeck上下文中引入了这种算法，这是针对特定的时间均匀扩散过程。因此，这里的目的是推广这种有效的数值方法，以便获得一般线性扩散的出口时间和位置的近似值。这种泛化的主要挑战是处理时间不均匀的扩散。通过理论结果和数值示例，特别小心地描述了该方法的效率。