Approximation of first passage times of switching diffusion

This paper studies the approximation of first passage time of a multi-dimensional switching diffusion process to a given target domain. We propose a discrete-time strong approximation scheme for switching diffusion processes with state-dependent switching rates. If τ and τh are the first passage times of the continuous and discretized processes respectively, then under some conditions we show that τh converges in distribution to τ as the discretization step tends to zero.