Free Access
Issue |
ESAIM: PS
Volume 21, 2017
|
|
---|---|---|
Page(s) | 220 - 234 | |
DOI | https://doi.org/10.1051/ps/2017006 | |
Published online | 12 December 2017 |
- F. Baccelli and G. Fayolle, Analysis of models reducible to a class of diffusion processes in the positive quarter plane. SIAM J. Appl. Math. 47 (1987) 1367–1385. [Google Scholar]
- O. Bernardi, M. Bousquet-Mélou and K. Raschel, Counting quadrant walks via Tutte’s invariant method. In 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2016) 203–214. [Google Scholar]
- M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane. In Algorithmic probability and combinatorics. Vol. 520 of Contemp. Math. Amer. Math. Soc. Providence, RI (2010) 1–39. [Google Scholar]
- K. Burdzy, Z.-Q. Chen, D. Marshall and K. Ramanan, Obliquely reflected Brownian motion in non-smooth planar domains. Ann. Probab. 45 (2017) 2971–3037. [Google Scholar]
- J. Dai, Steady-state analysis of reflected Brownian motions: Characterization, numerical methods and queueing applications. ProQuest LLC, Ann Arbor, MI. Ph.D. thesis, Stanford University (1990). [Google Scholar]
- J. Dai and A. Dieker, Nonnegativity of solutions to the basic adjoint relationship for some diffusion processes. Queueing Syst. 68 (2011) 295–303. [Google Scholar]
- J. Dai, S. Guettes and T. Kurtz, Characterization of the stationary distribution for a reflecting brownian motion in a convex polyhedron. Tech. Rep., Department of Mathematics, University of Wisconsin-Madison (2010). [Google Scholar]
- J. Dai and J. Harrison, Reflected Brownian motion in an orthant: numerical methods for steady-state analysis. Ann. Appl. Probab. 2 (1992) 65–86. [Google Scholar]
- J. Dai and T. Kurtz, Characterization of the stationary distribution for a semimartingale reflecting brownian motion in a convex polyhedron (1994). [Google Scholar]
- J. Dai and M. Miyazawa, Reflecting Brownian motion in two dimensions: Exact asymptotics for the stationary distribution. Stoch. Syst. 1 (2011)146–208. [Google Scholar]
- J. Dai and M. Miyazawa, Stationary distribution of a two-dimensional SRBM: geometric views and boundary measures. Queueing Syst. 74 (2013) 181–217. [Google Scholar]
- A. Dieker and J. Moriarty, Reflected Brownian motion in a wedge: sum-of-exponential stationary densities. Electron. Commun. Probab.14 (2009) 1–16. [CrossRef] [Google Scholar]
- G. Doetsch, Introduction to the theory and application of the Laplace transformation. Springer-Verlag, New York Heidelberg (1974). [Google Scholar]
- J. Dubédat, Reflected planar Brownian motions, intertwining relations and crossing probabilities. Ann. Inst. Henri Poincaré Probab. Statist. 40 (2004) 539–552. [CrossRef] [MathSciNet] [Google Scholar]
- P. Dupuis and R. Williams, Lyapunov functions for semimartingale reflecting Brownian motions. Ann. Probab. 22 (1994) 680–702. [Google Scholar]
- G. Fayolle, R. Iasnogorodski and V. Malyshev, Random Walks in the Quarter-Plane. Springer Berlin Heidelberg, Berlin, Heidelberg (1999). [Google Scholar]
- M. Foddy, Analysis of Brownian motion with drift, confined to a quadrant by oblique reflection (diffusions, Riemann-Hilbert problem). ProQuest LLC, Ann Arbor, MI. Ph.D. thesis, Stanford University (1984). [Google Scholar]
- G. Foschini, Equilibria for diffusion models of pairs of communicating computers–symmetric case. IEEE Trans. Inform. Theory 28 (1982) 273–284. [CrossRef] [Google Scholar]
- S. Franceschi and I. Kurkova, Asymptotic expansion for the stationary distribution of a reflected Brownian motion in the quarter plane. Preprint arXiv:1604.02918 (2016). [Google Scholar]
- S. Franceschi, I. Kurkova and K. Raschel, Analytic approach for reflected Brownian motion in the quadrant. In 27th Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA’16) (2016). [Google Scholar]
- J. Harrison and J. Hasenbein, Reflected Brownian motion in the quadrant: tail behavior of the stationary distribution. Queueing Syst. 61 (2009) 113–138. [Google Scholar]
- J. Harrison and M. Reiman, On the distribution of multidimensional reflected Brownian motion. SIAM J. Appl. Math. 41 (1981) 345–361. [Google Scholar]
- J. Harrison and R. Williams, Brownian models of open queueing networks with homogeneous customer populations. Stochastics 22 (1987a) 77–115. [CrossRef] [MathSciNet] [Google Scholar]
- J. Harrison and R. Williams, Multidimensional reflected Brownian motions having exponential stationary distributions. Ann. Probab. 15 (1987b) 115–137. [Google Scholar]
- D. Hobson and L. Rogers, Recurrence and transience of reflecting Brownian motion in the quadrant. In vol. 113 of Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge Univ Press (1993) 387–399 [Google Scholar]
- J.-F. Le Gall, Mouvement brownien, cônes et processus stables. Probab. Theory Related Fields 76 (1987) 587–627. [CrossRef] [Google Scholar]
- G. Litvinchuk, Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift. Springer Netherlands, Dordrecht (2000). [Google Scholar]
- V. Malyšev, An analytic method in the theory of two-dimensional positive random walks. Sibirsk. Mat. Ž. 13 (1972) 1314–1329, 1421. [Google Scholar]
- W. Tutte, Chromatic sums revisited. Aequationes Math. 50 (1995) 95–134. [CrossRef] [Google Scholar]
- R. Williams, Semimartingale reflecting Brownian motions in the orthant. In Stochastic networks. Vol. 71 of IMA Vol. Math. Appl. Springer, New York (1995) 125–137. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.