A note on the exponentiality of total hazards before failure (Q1112449)

If N is a univariate counting process with a given intensity it is well known that the ``time changed'' counting process \(\bar N(t)=N(A^{- 1}(t))\) is Poisson with unit parameter, if \(A^{-1}(t)\) is the inverse function of the integrand intensity A(t) of N up to time t. Meyer, Aalen, Hoen, Kurtz and Jacobson extended this result to multivariate counting processes with continuous compensators. The purpose of this note is to show that if the compensators are allowed to have jumps, this result holds in the limit, if the jumps of the compensators become uniformly small.