A Limit Theorem for a Class of Inhomogeneous Markov Processes
A Limit Theorem for a Class of Inhomogeneous Markov Processes
Let $\{X(t): t \in R^+ \text{or} I^+\}$ be an (aperiodic) irreducible Markov process with a finite state space $S$ and transition rate $q_{ij}(t) = p(i, j)(\lambda(t))^{U(i, j)}$, where $0 \leq U(i, j) \leq \infty$ and $\lambda(t)$ is some suitable rate function with $\lim_{t \rightarrow \infty}\lambda(t) = 0$. We shall show …