A diffusion model for two parallel queues with processor sharing: Transient behavior and asymptotics.
Knessl, Charles (1999)
Journal of Applied Mathematics and Stochastic Analysis
P. Mc Gill (1981)
Séminaire de probabilités de Strasbourg
Alfa, Attahiru Sule, Dolhun, K.Laurie, Chakravarthy, S. (1995)
Journal of Applied Mathematics and Stochastic Analysis
Pierre Étoré, Antoine Lejay (2007)
ESAIM: Probability and Statistics
In this paper, we prove a Donsker theorem for one-dimensional processes generated by an operator with measurable coefficients. We construct a random walk on any grid on the state space, using the transition probabilities of the approximated process, and the conditional average times it spends on each cell of the grid. Indeed we can compute these quantities by solving some suitable elliptic PDE problems.
Persi Diaconis, David Freedman (1987)
Annales de l'I.H.P. Probabilités et statistiques
Huillet, Thierry E. (2009)
Journal of Probability and Statistics
Nathalie Eisenbaum, Yueyun Hu (2003)
Annales de l'I.H.P. Probabilités et statistiques
Valentin Grecea (2011)
Open Mathematics
Given the (canonical) Markov process associated with a sufficiently general semigroup (P t), we establish a result concerning the uniform completeness of a family of L 2-spaces naturally associated with the jumps of the process. An application of this result is presented.
Hamza, Kais, Klebaner, Fima C. (2007)
Journal of Applied Mathematics and Stochastic Analysis
P.J. Fitzsimmons, R.K. Getoor (1991)
Mathematische Zeitschrift
Chakravarthy, S., Alfa, Attahiru Sule (1994)
Journal of Applied Mathematics and Stochastic Analysis
Jia-An Yan (1988)
Séminaire de probabilités de Strasbourg
Bercu, Bernard, Del Moral, Pierre, Doucet, Arnaud (2009)
Electronic Journal of Probability [electronic only]
A. Styszyński (1983)
Applicationes Mathematicae
Li, Wenbo V. (1999)
Electronic Communications in Probability [electronic only]
Burdzy, Krzysztof, White, David (2004)
Electronic Communications in Probability [electronic only]
Nathalie Eisenbaum (2002)
Séminaire de probabilités de Strasbourg
Gabriela I. Sebe (2002)
Journal de théorie des nombres de Bordeaux
Using the natural extensions for the Rosen maps, we give an infinite-order-chain representation of the sequence of the incomplete quotients of the Rosen fractions. Together with the ergodic behaviour of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion.
Saintier, Nicolas (2007)
Electronic Communications in Probability [electronic only]
Islam, Md.Shafiqul, Góra, Pawel, Boyarsky, Abraham (2005)
Journal of Applied Mathematics and Stochastic Analysis