Blanchet, J., Glynn, P., & Thorisson, H. (2015). On the Limiting Ratio of Current Age to Total Life for Null Recurrent Renewal Processes. ArXiv. /abs/1503.08374
Abstract
If the inter-arrival time distribution of a renewal process is regularly varying with index (i.e. the inter-arrival times have infinite mean) and if is the associated age process at time . Then we show that if is the length of the current cycle at time ,
where is . This extends a classical result in renewal theory in the finite mean case which indicates that the limit is .
Authors
Jose Blanchet, Peter Glynn, Hermann Thorisson
Publication date
2015/3/29
Journal
arXiv preprint arXiv:1503.08374
