The Annals of Probability
- Ann. Probab.
- Volume 17, Number 2 (1989), 723-736.
A Renewal Theory with Varying Drift
Let $R$ be the excess over the boundary in renewal theory. It is well known that $ER$ has a limit $r$ when the drift of the random walk $\mu \geq 0$. We study renewal theorems with varying $\mu$. Conditions are given under which the tail $ER - r$ is uniformly dominated by a decreasing integrable function for $\mu$ in a compact interval in $(0, \infty)$. Conditions are also given under which the derivative of the tail $(\partial/\partial\mu)(ER - r)$ is uniformly dominated by a directly Riemann integrable function.
Ann. Probab., Volume 17, Number 2 (1989), 723-736.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K05: Renewal theory
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Zhang, Cun-Hui. A Renewal Theory with Varying Drift. Ann. Probab. 17 (1989), no. 2, 723--736. doi:10.1214/aop/1176991423. https://projecteuclid.org/euclid.aop/1176991423