Partially exchangeable Markov chains and characterisation of multitype Lambda-coalescents

TL;DR

This paper characterizes multitype Lambda-coalescents with multiple switches through the study of partially exchangeable Markov chains, providing new insights into their transition rates, convergence, and duality properties.

Contribution

It introduces a novel characterization of multitype Lambda-coalescents with multiple switches using partially exchangeable Markov chains and analyzes their limiting frequency processes.

Findings

Characterization of admissible transition rates via particle motion decomposition

Convergence and duality results for the de Finetti measure process

Examples from recent literature illustrating the theory

Abstract

In this paper, we study consistent and partially exchangeable sequences of Markov chains on a finite state space. We provide a characterisation of the admissible transition rates via a decomposition into individual and coordinated motion of particles. As a consequence, we find a characterisation of multitype Lambda-coalescents with multiple switches. Moreover, we provide convergence and duality results for the corresponding process of limiting relative frequencies that we call the de Finetti measure process, and discuss a number of examples from the recent literature.