Elementary results on K processes with weights

TL;DR

This paper introduces a specific class of K processes with weights, explores their fundamental properties, and extends previous work by deriving new results on their Markovian nature, transition rates, and stationary distributions.

Contribution

It provides a new construction of K processes with weights and derives elementary properties, including cases not previously analyzed by Reuter.

Findings

Established the Markov property of the process

Derived transition rates and stationary distribution

Extended analysis to a new case not previously studied

Abstract

We introduce the title process via a particular construction, and relate it to processes previously studied, in particular a process introduced by G. E. H. Reuter in 1969. We derive elementary properties and quantities of this processes: Markov property, transition rates, stationary distribution, and the infinitesimal generator for a case not treated by Reuter.