## The Annals of Applied Probability

### Stability and nonproduct form of stochastic fluid networks with Lévy inputs

Offer Kella

#### Abstract

We consider a stochastic fluid network with inputs which are independent subordinators. We show that under some natural conditions the distribution of the fluid content process converges in total variation to a proper limit and that the limiting distribution has a positive mass at the origin. As a consequence of the methodology used, we obtain upper and lower bounds for the expected values of this limiting distribution. For the two-dimensional case, under certain conditions, explicit formulas for the means, variances and covariance of the steady-state fluid content are given. Further, for the two-dimensional case, it is shown that, other than for trivial setups, the limiting distribution cannot have product form.

#### Article information

Source
Ann. Appl. Probab. Volume 6, Number 1 (1996), 186-199.

Dates
First available in Project Euclid: 18 October 2002

http://projecteuclid.org/euclid.aoap/1034968070

Digital Object Identifier
doi:10.1214/aoap/1034968070

Mathematical Reviews number (MathSciNet)
MR1389836

Zentralblatt MATH identifier
0863.60070

#### Citation

Kella, Offer. Stability and nonproduct form of stochastic fluid networks with Lévy inputs. Ann. Appl. Probab. 6 (1996), no. 1, 186--199. doi:10.1214/aoap/1034968070. http://projecteuclid.org/euclid.aoap/1034968070.

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• MOUNT SCOPUS, JERUSALEM 91905 ISRAEL E-mail: mskella@olive.mscc.huji.ac.il