Abstract
We develop methods for the computation of some distribution functions or their Laplace transforms, associated with a time homogeneous diffusion with killing under the assumption that its generator and the killing-rate function are piece-wise constant. The main result is the representation of the Laplace-transform of the joint distribution of the killing time and of the state at killing. In particular, it is shown that the marginal density of the state at killing has an explicit representation. We also consider the computation of the analogous distributions for a countable time-homogeneous Markov chain with killing. This work was motivated by applications of Markov processes to model the evolution of markers; see Jewell and Kalbfleisch[3]
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