A non-linear Renewal Theorem with stationary and slowly changing perturbations
نویسندگان
چکیده
Abstract: Non-linear renewal theory is extended to include random walks perturbed by both a slowly changing sequence and a stationary one. Main results include a version of the Key Renewal Theorem, a derivation of the limiting distribution of the excess over a boundary, and an expansion for the expected first passage time. The formulation is motivated by problems in sequential analysis with staggered entry, where subjects enter a study at random times.
منابع مشابه
The Key Renewal Theorem for a Transient Markov Chain
provided Eξ1 is finite and positive (see, for example, Feller and Orey [8], Feller [7, Ch. XI], Woodroofe [25, Appendix]); F is called lattice if it is concentrated on some lattice {ka, k ∈ Z} with a > 0. If F is lattice the same is true when h is a multiple of the span a. It is proved in Wang and Woodroofe [23] and in Borovkov and Foss [5, Theorem 2.6] that (1) holds uniformly over certain cla...
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تاریخ انتشار 2006