On the probability distribution of additive functionals of jump Markov processes
Résumé
In this paper, an additive functional $\{Y_t, t ≥ 0\}$ (with continuous and discontinuous parts) of a jump Markov process $\{X_t, t ≥ 0\}$ is considered. We provide a simple estimate of the probability distribution of the random variable $(Y_t, X_t )$. As a result, its distribution function is shown to be essentially the solution of a partial differential equation.