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 ...

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 obtain a Lamperti type representation for real-valued self-similar Markov processes, killed at their hitting time of zero. Namely, we represent real-valued self-similar Markov ...