Jump diffusion approximation for a Markovian transport model

In this note we analyze a Markovian model for particle transport in a fluidized bed chemical reactor, and prove a diffusion approximation. The transport model is basically a birth-death Markov process with reflection at the origin and occasional jumps to the origin, modelling transport in the wakes of rising fluidization bubbles. We establish here a strong approximation by a jump diffusion process with trajectory-dependent jump times.