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December, 1975 A Local Time for a Storage Process
Erhan Cinlar
Ann. Probab. 3(6): 930-950 (December, 1975). DOI: 10.1214/aop/1176996220

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 $r$.

Citation

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Erhan Cinlar. "A Local Time for a Storage Process." Ann. Probab. 3 (6) 930 - 950, December, 1975. https://doi.org/10.1214/aop/1176996220

Information

Published: December, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0328.60042
MathSciNet: MR391279
Digital Object Identifier: 10.1214/aop/1176996220

Subjects:
Primary: 60J55
Secondary: 60H20

Keywords: Local times , Markov processes , regenerative events , storage theory

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 6 • December, 1975
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