Abstract
The concept of the renewal property is extended to processes indexed by a multidimensional time
parameter. The definition given includes not only partial sum processes, but also Poisson processes and
many other point processes whose jump points are not totally ordered. A new version of the waiting time
paradox is proven for multidimensional Poisson processes, and is shown to imply the renewal property.
Finally, martingale properties of renewal processes are studied.
| Original language | American English |
|---|---|
| Pages (from-to) | 411-441 |
| Journal | Stochastics: An International Journal of Probability and Stochastic Processes (formerly Stochastics and Stochastic Reports) |
| Volume | 78 |
| Issue number | 6 |
| State | Published - 2006 |