On the Distribution of the First Component ηt of a Controlled Poisson Process {ηt, ξt}, t ≥ 0, without Boundary

详细

An ergodicity condition for the first component ηt of a controlled Poisson process without boundary is found. The Laplace transform of the same component η_t, t ≥ 0, is obtained from the given transition probabilities of the process {η_t, ξ_t}, t ≥ 0. It is essential that the given process {η_t, ξ_t}, t ≥ 0, is a Markov process homogeneous in the second component.