Superposition of renewal processes in a random environment

A random environment is modeled by an arbitrary stochastic process, the future of which is described by a [sigma]-algebra. Baxter and Li (1994) discussed generalizations of standard limit theorems of renewal theory to the case where a random environment is involved. In this paper, we consider superposition of renewal processes in a random environment. In particular, the central limit theorem and other limiting properties of superposition of renewal processes in a random environment are derived.Central limit theorem Residual life Current life [sigma]-algebra Reverse martingale