Measure-branching renewal processes

Consider a generalized renewal process where elements are replaced by a random number of new elements. The corresponding generalization of the residual lifetime at t is a random measure [mu]t(du) on [0, [infinity]). The measure-valued process {[mu]t(du), t >= 0} is a homogeneous Markov process. We obtain a measure-branching approximation for {n-1 [mu]Tt(T du), t >= 0} as n --> [infinity] and T = T(n) --> [infinity].General branching process Immigration Residual lifetime Measure-branching process