Bivariate Markov chains converging to Lamperti transform Markov Additive Processes

Bénédicte Haas, Robin Stephenson

Motivated by various applications, we describe the scaling limits of bivariate Markov chains $(X,J)$ on ${\mathbb{Z}}_{+}\times \{1,\dots ,\kappa \}$ where $X$ can be viewed as a position ma…