solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看4320次
A martingale view of Blackwell's renewal theorem and its extensions to a general counting process. (arXiv:1712.06278v1 [math.PR])
来源于:arXiv
Martingales constitute a basic tool in stochastic analysis; this paper
considers their application to counting processes. We use this tool to revisit
a renewal theorem and its extensions for various counting processes. We first
consider a renewal process as a pilot example, deriving a new semimartingale
representation that differs from the standard decomposition via the stochastic
intensity function. We then revisit Blackwell's renewal theorem, its
refinements and extensions. Based on these observations, we extend the
semimartingale representation to a general counting process, and give
conditions under which asymptotic behaviour similar to Blackwell's renewal
theorem holds. 查看全文>>