On meeting and merging of stochastic flow of non-homogeneous Markov and semi-Markov dynamics

Abstract

We consider a general class of semi-Markov processes on countable state-space, with a differentiable kernel such that the embedded Markov chain may not be homogeneous. Using an SDE representation of the process, we study the associated flow by investigating meetings and merging related events for solutions, starting with different initial conditions. Some sufficient conditions for almost sure meeting and merging are also obtained. Many examples are considered to clarify the intricacies and implications of this study.