The Annals of Probability

A Local Time for a Storage Process

Erhan Cinlar

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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


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