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References

  1. Anderson, Robert F.; Orey, Steven. Small random perturbation of dynamical systems with reflecting Nagoya Math. J. 60 (1976), 189--216. MR0397893 (53 #1749)
  2. Aubin, Jean-Pierre; Frankowska, Hélène. Set-valued analysis. Systems & Control: Foundations & Applications, 2. Birkhäuser Boston, Inc., Boston, MA, 1990. xx+461 pp. ISBN: 0-8176-3478-9 MR1048347 (91d:49001)
  3. Bichteler, Klaus. Stochastic integration and $Lsp{p}$-theory of semimartingales. Ann. Probab. 9 (1981), no. 1, 49--89. MR0606798 (82g:60071)
  4. Bernard, Alain; el Kharroubi, Ahmed. Régulations déterministes et stochastiques dans le premier Rsp n$] Stochastics Stochastics Rep. 34 (1991), no. 3-4, 149--167. MR1124833 (92k:60178)
  5. Billingsley, Patrick. Convergence of probability measures. John Wiley & Sons, Inc., New York-London-Sydney 1968 xii+253 pp. MR0233396 (38 #1718)
  6. Borodin, Andrei N.; Salminen, Paavo. Handbook of Brownian motion---facts and formulae. Probability and its Applications. Birkhäuser Verlag, Basel, 1996. xiv+462 pp. ISBN: 3-7643-5463-1 MR1477407 (98i:60077)
  7. V. Burenkov. Sobolev Spaces on Domains. Teubner-Texte zur Mathematik, Leipzig, 1998.
  8. Burdzy, Krzysztof; Toby, Ellen. A Skorohod-type lemma and a decomposition of reflected Brownian Ann. Probab. 23 (1995), no. 2, 586--604. MR1334162 (96i:60045)
  9. Chen, Zhen Qing. On reflected Dirichlet spaces. Probab. Theory Related Fields 94 (1992), no. 2, 135--162. MR1191106 (93m:31014)
  10. Chen, Zhen Qing. On reflecting diffusion processes and Skorokhod decompositions. Probab. Theory Related Fields 94 (1993), no. 3, 281--315. MR1198650 (94b:60090)
  11. Chen, Hong; Mandelbaum, Avi. Discrete flow networks: bottleneck analysis and fluid Math. Oper. Res. 16 (1991), no. 2, 408--446. MR1106809 (92b:60090)
  12. Costantini, C.. The Skorohod oblique reflection problem in domains with corners and Probab. Theory Related Fields 91 (1992), no. 1, 43--70. MR1142761 (93e:60109)
  13. J. Dai and R. Williams. Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons. Theor. Probab. Appl., 50:3-53, 1995.
  14. DeBlassie, R. Dante. Explicit semimartingale representation of Brownian motion in a Stochastic Process. Appl. 34 (1990), no. 1, 67--97. MR1039563 (91h:60091)
  15. DeBlassie, R. Dante; Toby, Ellen H. Reflecting Brownian motion in a cusp. Trans. Amer. Math. Soc. 339 (1993), no. 1, 297--321. MR1149119 (93k:60199)
  16. DeBlassie, R. Dante; Toby, Ellen H. On the semimartingale representation of reflecting Brownian motion in a Probab. Theory Related Fields 94 (1993), no. 4, 505--524. MR1201557 (94a:60118)
  17. Doob, J. L. Measure theory. Graduate Texts in Mathematics, 143. Springer-Verlag, New York, 1994. xii+210 pp. ISBN: 0-387-94055-3 MR1253752 (95c:28001)
  18. Dupuis, Paul; Ishii, Hitoshi. On Lipschitz continuity of the solution mapping to the Skorokhod Stochastics Stochastics Rep. 35 (1991), no. 1, 31--62. MR1110990 (93e:60110)
  19. Dupuis, Paul; Ishii, Hitoshi. On oblique derivative problems for fully nonlinear second-order Hokkaido Math. J. 20 (1991), no. 1, 135--164. MR1096165 (92b:35060)
  20. Kushner, Harold J.; Dupuis, Paul G. Numerical methods for stochastic control problems in continuous Applications of Mathematics (New York), 24. Springer-Verlag, New York, 1992. x+439 pp. ISBN: 0-387-97834-8 MR1217486 (94e:93005)
  21. Dupuis, Paul; Ramanan, Kavita. A Skorokhod problem formulation and large deviation analysis of a Queueing Systems Theory Appl. 28 (1998), no. 1-3, 109--124. MR1628485 (99c:60201)
  22. Dupuis, Paul; Ramanan, Kavita. Convex duality and the Skorokhod problem. I, II. Probab. Theory Related Fields 115 (1999), no. 2, 153--195, 197--236. MR1720348 (2001f:49041)
  23. Dupuis, Paul; Ramanan, Kavita. Convex duality and the Skorokhod problem. I, II. Probab. Theory Related Fields 115 (1999), no. 2, 153--195, 197--236. MR1720348 (2001f:49041)
  24. Dupuis, Paul; Ramanan, Kavita. A multiclass feedback queueing network with a regular Skorokhod Queueing Syst. 36 (2000), no. 4, 327--349. MR1823974 (2002g:60143)
  25. Freidlin, Mark. Functional integration and partial differential equations. Annals of Mathematics Studies, 109. Princeton University Press, Princeton, NJ, 1985. x+545 pp. ISBN: 0-691-08354-1; 0-691-08362-2 MR0833742 (87g:60066)
  26. Fukushima, Masatoshi; =Oshima, Y=oichi; Takeda, Masayoshi. Dirichlet forms and symmetric Markov processes. de Gruyter Studies in Mathematics, 19. Walter de Gruyter & Co., Berlin, 1994. x+392 pp. ISBN: 3-11-011626-X MR1303354 (96f:60126)
  27. Harrison, J. Michael; Reiman, Martin I. Reflected Brownian motion on an orthant. Ann. Probab. 9 (1981), no. 2, 302--308. MR0606992 (82c:60141)
  28. Holmes, Richard B. Smoothness of certain metric projections on Hilbert space. Trans. Amer. Math. Soc. 184 (1973), 87--100. MR0326252 (48 #4596)
  29. Kallenberg, Olav. Foundations of modern probability. Probability and its Applications (New York). Springer-Verlag, New York, 1997. xii+523 pp. ISBN: 0-387-94957-7 MR1464694 (99e:60001)
  30. Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1988. xxiv+470 pp. ISBN: 0-387-96535-1 MR0917065 (89c:60096)
  31. Kwon, Y.; Williams, R. J.. Reflected Brownian motion in a cone with radially homogeneous Trans. Amer. Math. Soc. 327 (1991), no. 2, 739--780. MR1028760 (92a:60174)
  32. Lions, P.-L.; Sznitman, A.-S. Stochastic differential equations with reflecting boundary Comm. Pure Appl. Math. 37 (1984), no. 4, 511--537. MR0745330 (85m:60105)
  33. A. Mandelbaum and A. Van der Heyden. Complementarity and reflection. Unpublished work, 1987.
  34. Moreau, Jean-Jacques. Proximitéet dualité dans un espace hilbertien. (French) Bull. Soc. Math. France 93 1965 273--299. MR0201952 (34 #1829)
  35. Parthasarathy, K. R. Probability measures on metric spaces. Probability and Mathematical Statistics, No. 3 Academic Press, Inc., New York-London 1967 xi+276 pp. MR0226684 (37 #2271)
  36. Ramanan, Kavita; Reiman, Martin I. Fluid and heavy traffic diffusion limits for a generalized processor Ann. Appl. Probab. 13 (2003), no. 1, 100--139. MR1951995 (2004b:60220)
  37. K. Ramanan and M.I. Reiman. The heavy traffic limit of an unbalanced generalized processor sharing model. Preprint, 2005.
  38. Reiman, M. I.; Williams, R. J.. A boundary property of semimartingale reflecting Brownian motions. Probab. Theory Related Fields 77 (1988), no. 1, 87--97. MR0921820 (89a:60191)
  39. Rockafellar, R. Tyrrell. Convex analysis. Princeton Mathematical Series, No. 28 Princeton University Press, Princeton, N.J. 1970 xviii+451 pp. MR0274683 (43 #445)
  40. Royden, H. L. Real analysis. The Macmillan Co., New York; Collier-Macmillan Ltd., London 1963 xvi+284 pp. MR0151555 (27 #1540)
  41. Saisho, Yasumasa. Stochastic differential equations for multidimensional domain with Probab. Theory Related Fields 74 (1987), no. 3, 455--477. MR0873889 (88b:60139)
  42. A.V. Skorokhod. Stochastic equations for diffusions in a bounded region. Theor. of Probab. and its Appl., 6:264--274, 1961.
  43. Stroock, Daniel W.; Varadhan, S. R. S. Diffusion processes with boundary conditions. Comm. Pure Appl. Math. 24 1971 147--225. MR0277037 (43 #2774)
  44. Tanaka, Hiroshi. Stochastic differential equations with reflecting boundary condition in Hiroshima Math. J. 9 (1979), no. 1, 163--177. MR0529332 (80k:60075)
  45. Taylor, L. M.; Williams, R. J.. Existence and uniqueness of semimartingale reflecting Brownian motions Probab. Theory Related Fields 96 (1993), no. 3, 283--317. MR1231926 (94m:60161)
  46. Varadhan, S. R. S.; Williams, R. J.. Brownian motion in a wedge with oblique reflection. Comm. Pure Appl. Math. 38 (1985), no. 4, 405--443. MR0792398 (87c:60066)
  47. Whitt, Ward. Stochastic-process limits. Springer Series in Operations Research. Springer-Verlag, New York, 2002. xxiv+602 pp. ISBN: 0-387-95358-2 MR1876437 (2003f:60005)
  48. Williams, R. J.. Reflected Brownian motion in a wedge: semimartingale property. Z. Wahrsch. Verw. Gebiete 69 (1985), no. 2, 161--176. MR0779455 (86h:60164)
  49. Williams, R. J.. Semimartingale reflecting Brownian motions in the orthant. 125--137, IMA Vol. Math. Appl., 71, Springer, New York, 1995. MR1381009 (96k:60213)


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