Markov processes form a fundamental class of stochastic models in which the evolution of a system is delineated by the memoryless property. In such processes, the future state depends solely on the ...

Quasi-stationary distributions (QSDs) offer a compelling framework for understanding the long-term behaviour of Markov processes that possess an absorbing state. In many natural and engineered systems ...

Let $X = (X_t, P^x)$ be a right Markov process and let $m$ be an excessive measure for $X$. Associated with the pair $(X, m)$ is a stationary strong Markov process ...

In this paper we show that any separable stochastic process on a compact metric space can be derived from a temporally homogeneous Markov process on the extreme points of a compact convex set of ...