Stochastically monotone Markov chains form an important wide class of Markov processes. This project addresses the discrete case both in time and the state space. Our initial observation is that a family of monotonely coupled chains could be treated as an infinite particle system with dependent reproduction.
Paper 1. Sagitov
S. and Jagers. J. Rank-dependent Galton-Watson
processes and their pathwise duals. Preprint. Submitted in September