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 $r$.
Publié le : 1975-12-14
Classification:
Local times,
regenerative events,
storage theory,
Markov processes,
60J55,
60H20
@article{1176996220,
author = {Cinlar, Erhan},
title = {A Local Time for a Storage Process},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 930-950},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996220}
}
Cinlar, Erhan. A Local Time for a Storage Process. Ann. Probab., Tome 3 (1975) no. 6, pp. 930-950. http://gdmltest.u-ga.fr/item/1176996220/