Dupuis and Williams proved that a sufficient condition for the
positive recurrence and the existence of a unique stationary distribution for a
semimartingale reflecting Brownian motion in an orthant (SRBM) is that all
solutions of an associated deterministic Skorohod problem are attracted to the
origin. In this paper, we derive a sufficient condition under which we can
construct an explicit linear Lyapunov function for the Skorohod problem. Thus,
this implies a sufficient condition for the stability of the deterministic
Skorohod problem. The existence of such a linear Lyapunov function is
equivalent to the feasibility of a set of linear inequalities. In the
two-dimensional case, we recover the necessary and sufficient conditions for
the positive recurrence. Some explicit sufficient conditions are derived for
the higher-dimensional case.
Publié le : 1996-08-14
Classification:
Semimartingale reflecting Brownian motion on an orthant,
positive recurrence,
stationary distribution,
linear Lyapunov function,
fluid network,
60J60,
60J65,
60K25,
34D20
@article{1034968226,
author = {Chen, Hong},
title = {A sufficient condition for the positive recurrence of a
semimartingale reflecting Brownian motion in an orthant},
journal = {Ann. Appl. Probab.},
volume = {6},
number = {1},
year = {1996},
pages = { 758-765},
language = {en},
url = {http://dml.mathdoc.fr/item/1034968226}
}
Chen, Hong. A sufficient condition for the positive recurrence of a
semimartingale reflecting Brownian motion in an orthant. Ann. Appl. Probab., Tome 6 (1996) no. 1, pp. 758-765. http://gdmltest.u-ga.fr/item/1034968226/