## The Annals of Probability

- Ann. Probab.
- Volume 3, Number 6 (1975), 930-950.

### A Local Time for a Storage Process

#### Abstract

Content process $X$ of a continuous store satisfies $X_t = X_0 + A_t - \int^t_0 r(X_s) ds, t \geqq 0$. Here, $A$ has nonnegative stationary independent increments, and $r$ is a nondecreasing continuous function. The solution $X$ is a Hunt process. Paper considers the local time $L$ of $X$ at $0$. $L$ may be the occupation time of $\{0\}$ if the latter is not zero identically. The more interesting case is where the occupation time of $\{0\}$ is zero but 0 is regular for $\{0\}$; then $L$ is constructed as the limit of a sequence of weighted occupation times of $\{0\}$ for a sequence of Hunt processes $X^n$ approximating $X$. The $\lambda$-potential of $L$ is computed in terms of the Levy measure of $A$ and the function $r$.

#### Article information

**Source**

Ann. Probab., Volume 3, Number 6 (1975), 930-950.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176996220

**Digital Object Identifier**

doi:10.1214/aop/1176996220

**Mathematical Reviews number (MathSciNet)**

MR391279

**Zentralblatt MATH identifier**

0328.60042

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60J55: Local time and additive functionals

Secondary: 60H20: Stochastic integral equations

**Keywords**

Local times regenerative events storage theory Markov processes

#### Citation

Cinlar, Erhan. A Local Time for a Storage Process. Ann. Probab. 3 (1975), no. 6, 930--950. doi:10.1214/aop/1176996220. https://projecteuclid.org/euclid.aop/1176996220