Identify whether abstract intertwined limiting processes are limits of the finite processes

Determine whether the limiting process constructed abstractly by the Borodin–Olshanski intertwining framework is a scaling limit of the corresponding family of finite intertwined Markov processes.

Background

The paper discusses families of Markov processes linked by intertwining relations and the Borodin–Olshanski construction of a process on a natural limiting space. That construction establishes existence under suitable hypotheses, but it is abstract and does not by itself identify the limiting process as the limit of the finite-level processes.

The authors’ framework proves convergence for the particular families treated in the paper, while noting that the analogous convergence question remains unresolved in the more general Borodin–Olshanski setting.