Multivariate survival distributions of age and residual lifetime processes in nonhomogenous poisson process

Abstract

Let {N(t), t≥0} be the nonhomogenous Poisson process with cumulative intensity parameter Ν (t), {δt,t ⩾ 0} the age process, and {γt,t ⩾ 0} the residual lifetime process. In the present paper the expression of n-dimensional survival distribution functions of the processes {δt} and {γt}, and their Lebesgue decompositions are derived.