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Volumn 11, Issue , 2006, Pages 934-992

Reflected diffusions defined via the extended skorokhod map

Author keywords

Extended Skorohod problem; Extended Skorokhod map; Generalised processor sharing; Reflected Brownian motion; Reflected diffusions; Reflection map; Semimartingales; Skorokhod map; Skorokhod problem; Stochastic differential equations with reflection; Strong solutions; Submartingale problem

Indexed keywords


EID: 33751038195     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v11-360     Document Type: Article
Times cited : (47)

References (49)
  • 1
    • 84972544415 scopus 로고
    • Small random perturbations of dynamical systems with reflecting boundary
    • R. Anderson and S. Orey. Small random perturbations of dynamical systems with reflecting boundary. Nagoya Math. J, 60:189-216, 1976.
    • (1976) Nagoya Math. J , vol.60 , pp. 189-216
    • Anderson, R.1    Orey, S.2
  • 3
    • 0346199076 scopus 로고
    • Stochastic integration and Lp-theory of semimartingales
    • K. Bichteler. Stochastic integration and Lp-theory of semimartingales. Ann. Probab., 9:4989, 1981.
    • (1981) Ann. Probab , vol.9 , pp. 4989
    • Bichteler, K.1
  • 4
    • 0001719528 scopus 로고
    • Regulations de processus dans le premier orthant de Rn
    • A. Bernard and A. El Kharroubi. Regulations de processus dans le premier orthant de Rn. Stoch. Stoch. Rep, 34:149-167, 1991.
    • (1991) Stoch. Stoch. Rep , vol.34 , pp. 149-167
    • Bernard, A.1    El Kharroubi, A.2
  • 8
    • 2142655844 scopus 로고
    • A Skorohod-type lemma and a decomposition of reflected Brownian motion
    • K. Burdzy and E. Toby. A Skorohod-type lemma and a decomposition of reflected Brownian motion. Ann. Of Probab., 23:586-604, 1995.
    • (1995) Ann. Of Probab , vol.23 , pp. 586-604
    • Burdzy, K.1    Toby, E.2
  • 9
    • 21144467150 scopus 로고
    • On reflected Dirichlet spaces
    • Z.-Q. Chen. On reflected Dirichlet spaces. Probab. Theor. Rel. Fields, 94:135-162, 1992.
    • (1992) Probab. Theor. Rel. Fields , vol.94 , pp. 135-162
    • Chen, Z.-Q.1
  • 10
    • 21144477966 scopus 로고
    • On reflecting diffusion processes and Skorokhod decompositions
    • Z.-Q. Chen. On reflecting diffusion processes and Skorokhod decompositions. Probab. Theor. Rel. Fields, 94:281-315, 1993.
    • (1993) Probab. Theor. Rel. Fields , vol.94 , pp. 281-315
    • Chen, Z.-Q.1
  • 11
    • 0000658047 scopus 로고
    • Discrete flow networks: Bottleneck analysis and fluid approximations
    • H. Chen and A. Mandelbaum. Discrete flow networks: bottleneck analysis and fluid approximations. Math. Of Oper. Res., 16:408-446, 1991.
    • (1991) Math. Of Oper. Res , vol.16 , pp. 408-446
    • Chen, H.1    Mandelbaum, A.2
  • 12
    • 0011769209 scopus 로고
    • The Skorokhod oblique reflection problem in domains with corners and applications to stochastic differential equations
    • C. Costantini. The Skorokhod oblique reflection problem in domains with corners and applications to stochastic differential equations. Probab. Theor. Rel. Fields, 91:43-70, 1992.
    • (1992) Probab. Theor. Rel. Fields , vol.91 , pp. 43-70
    • Costantini, C.1
  • 13
    • 0002611604 scopus 로고
    • Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons
    • J. Dai and R. Williams. Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons. Theor. Probab. Appl., 50:3-53, 1995.
    • (1995) Theor. Probab. Appl , vol.50 , pp. 3-53
    • Dai, J.1    Williams, R.2
  • 14
    • 0009088158 scopus 로고
    • Explicit semimartingale representation of Brownian motion in a wedge
    • R. D. DeBlassie. Explicit semimartingale representation of Brownian motion in a wedge. Stoch. Proc. Appl. 34:67-97, 1990.
    • (1990) Stoch. Proc. Appl , vol.34 , pp. 67-97
    • Deblassie, R.D.1
  • 15
    • 84968501871 scopus 로고
    • Reflecting Brownian motion in a cusp
    • R. D. DeBlassie and E. H. Toby. Reflecting Brownian motion in a cusp. Trans. Amer. Math. Soc., 339:297-321, 1993.
    • (1993) Trans. Amer. Math. Soc , vol.339 , pp. 297-321
    • Deblassie, R.D.1    Toby, E.H.2
  • 16
    • 21144478361 scopus 로고
    • On the semimartingale representation of reflecting Brownian motion in a cusp
    • R. D. DeBlassie and E. H. Toby. On the semimartingale representation of reflecting Brownian motion in a cusp. Probab. Theor. Rel. Fields, 94:505-524, 1993.
    • (1993) Probab. Theor. Rel. Fields , vol.94 , pp. 505-524
    • Deblassie, R.D.1    Toby, E.H.2
  • 17
    • 0004179052 scopus 로고
    • Springer-Verlag, New York
    • J. L. Doob. Measure Theory. Springer-Verlag, New York, 1993.
    • (1993) Measure Theory
    • Doob, J.L.1
  • 18
    • 0001985427 scopus 로고
    • On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications
    • P. Dupuis and H. Ishii. On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Stochastics, 35:31-62, 1991.
    • (1991) Stochastics , vol.35 , pp. 31-62
    • Dupuis, P.1    Ishii, H.2
  • 19
    • 84972529992 scopus 로고
    • On oblique derivative problems for fully nonlinear second-order elliptic PDEs on domains with corners
    • P. Dupuis and H. Ishii. On oblique derivative problems for fully nonlinear second-order elliptic PDEs on domains with corners. Hokkaido Math. J., 20:135-164, 1991.
    • (1991) Hokkaido Math. J , vol.20 , pp. 135-164
    • Dupuis, P.1    Ishii, H.2
  • 21
    • 0032396011 scopus 로고    scopus 로고
    • A Skorokhod problem formulation and large deviation analysis of a processor sharing model
    • P. Dupuis and K. Ramanan. A Skorokhod problem formulation and large deviation analysis of a processor sharing model. Queueing Systems, 28:109-124, 1998.
    • (1998) Queueing Systems , vol.28 , pp. 109-124
    • Dupuis, P.1    Ramanan, K.2
  • 23
    • 0033438733 scopus 로고    scopus 로고
    • Convex duality and the Skorokhod Problem-II
    • P. Dupuis and K. Ramanan. Convex duality and the Skorokhod Problem-II. Probab. Theor. And Rel. Fields, 115:197-236, 1999.
    • (1999) Probab. Theor. And Rel. Fields , vol.115 , pp. 197-236
    • Dupuis, P.1    Ramanan, K.2
  • 24
    • 0034355435 scopus 로고    scopus 로고
    • A multiclass feedback queueing network with a regular Skorokhod Problem
    • P. Dupuis and K. Ramanan. A multiclass feedback queueing network with a regular Skorokhod Problem. Queueing Systems, 36:327-349, 2000.
    • (2000) Queueing Systems , vol.36 , pp. 327-349
    • Dupuis, P.1    Ramanan, K.2
  • 25
    • 0003200789 scopus 로고
    • Functional Integration and Partial Differential Equations
    • Princeton University Press, Princeton
    • M. Freidlin. Functional Integration and Partial Differential Equations. Annals of Mathematics Studies Vol. 109, Princeton University Press, Princeton, 1985.
    • (1985) Annals of Mathematics Studies , vol.109
    • Freidlin, M.1
  • 26
    • 0003228611 scopus 로고
    • Dirichlet Forms and Symmetric Markov Processes
    • Walter de Gruyter, Berlin and Hawthorne, NY
    • M. Fukushima, Y. Oshima and M. Takeda. Dirichlet Forms and Symmetric Markov Processes. de Gruyter Studies in Math, vol. 19, Walter de Gruyter, Berlin and Hawthorne, NY, 1994.
    • (1994) De Gruyter Studies in Math , vol.19
    • Fukushima, M.1    Oshima, Y.2    Takeda, M.3
  • 27
    • 0000585232 scopus 로고
    • Reflected Brownian motion on an orthant
    • J.M. Harrison and M.I. Reiman. Reflected Brownian motion on an orthant. Ann. Of Probab., 9:302-308, 1981.
    • (1981) Ann. Of Probab , vol.9 , pp. 302-308
    • Harrison, J.M.1    Reiman, M.I.2
  • 28
    • 84966219708 scopus 로고
    • Smoothness of certain metric projections on Hilbert space
    • R. B. Holmes. Smoothness of certain metric projections on Hilbert space. Trans. Of Amer. Math. Soc., 184:87-100, 1973.
    • (1973) Trans. Of Amer. Math. Soc , vol.184 , pp. 87-100
    • Holmes, R.B.1
  • 31
    • 0009332551 scopus 로고
    • Reflected Brownian motion in a cone with radially homogeneous reflection field
    • Y. Kwon and R. J. Williams. Reflected Brownian motion in a cone with radially homogeneous reflection field. Trans. Of the AMS, 327:739-779, 1991.
    • (1991) Trans. Of the AMS , vol.327 , pp. 739-779
    • Kwon, Y.1    Williams, R.J.2
  • 32
    • 84990576543 scopus 로고
    • Stochastic differential equations with reflecting boundary conditions
    • P. L. Lions and A. S. Sznitman. Stochastic differential equations with reflecting boundary conditions. Comm. Pure and Appl. Math., 37:511-553, 1984.
    • (1984) Comm. Pure and Appl. Math , vol.37 , pp. 511-553
    • Lions, P.L.1    Sznitman, A.S.2
  • 34
    • 0000276924 scopus 로고
    • Proximite et dualite dans un espace Hilbertian
    • J. Moreau. Proximite et dualite dans un espace Hilbertian. Bull. Soc. Math. France, 93:273-299, 1965.
    • (1965) Bull. Soc. Math. France , vol.93 , pp. 273-299
    • Moreau, J.1
  • 36
    • 0037277890 scopus 로고    scopus 로고
    • Fluid and heavy traffic diffusion limits for a generalized processor sharing model
    • K. Ramanan and M. I. Reiman. Fluid and heavy traffic diffusion limits for a generalized processor sharing model. Ann. Of App. Probab., 1:100-139, 2003.
    • (2003) Ann. Of App. Probab , vol.1 , pp. 100-139
    • Ramanan, K.1    Reiman, M.I.2
  • 38
    • 0002800360 scopus 로고
    • A boundary property of semimartingale reflecting Brownian motions
    • M. I. Reiman and R. J. Williams. A boundary property of semimartingale reflecting Brownian motions. Probab. Theor. Rel. Fields, 77:87-97, 1988.
    • (1988) Probab. Theor. Rel. Fields , vol.77 , pp. 87-97
    • Reiman, M.I.1    Williams, R.J.2
  • 39
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton
    • R.T. Rockafellar. Convex Analysis. Princeton University Press, Princeton, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 40
    • 0003655416 scopus 로고
    • Macmillan Publishing Company, New York
    • H. L. Royden. Real Analysis. Macmillan Publishing Company, New York, 1989.
    • (1989) Real Analysis
    • Royden, H.L.1
  • 41
    • 0000605830 scopus 로고
    • Stochastic Differential Equations for Multi-dimensional Domain with Reflecting Boundary Probab
    • Y. Saisho. Stochastic Differential Equations for Multi-dimensional Domain with Reflecting Boundary Probab. Theor. Rel. Fields, 74:455-477, 1987.
    • (1987) Theor. Rel. Fields , vol.74 , pp. 455-477
    • Saisho, Y.1
  • 42
    • 0001379748 scopus 로고
    • Stochastic equations for diffusions in a bounded region
    • A.V. Skorokhod. Stochastic equations for diffusions in a bounded region. Theor. Of Probab. And its Appl., 6:264-274, 1961.
    • (1961) Theor. Of Probab. And Its Appl , vol.6 , pp. 264-274
    • Skorokhod, A.V.1
  • 43
    • 84980153169 scopus 로고
    • Diffusion processes with boundary conditions
    • D. W. Stroock and S. R. S. Varadhan. Diffusion processes with boundary conditions. Comm. Pure Appl. Math, 24:147-225, 1971.
    • (1971) Comm. Pure Appl. Math , vol.24 , pp. 147-225
    • Stroock, D.W.1    Varadhan, S.R.S.2
  • 44
    • 84972526612 scopus 로고
    • Stochastic differential equations with reflecting boundary conditions in convex regions
    • H. Tanaka. Stochastic differential equations with reflecting boundary conditions in convex regions. Hiroshima Math. J, 9:163-177, 1979.
    • (1979) Hiroshima Math. J , vol.9 , pp. 163-177
    • Tanaka, H.1
  • 45
    • 21144473462 scopus 로고
    • Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant
    • L. M. Taylor and R. J. Williams. Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant. Probab. Theor. Rel. Fields, 96:283-317, 1993.
    • (1993) Probab. Theor. Rel. Fields , vol.96 , pp. 283-317
    • Taylor, L.M.1    Williams, R.J.2
  • 46
    • 0005696341 scopus 로고
    • Brownian motion in a wedge with oblique reflection
    • S. R. S. Varadhan and R. J. Williams. Brownian motion in a wedge with oblique reflection. Comm. Pure Appl. Math., 24:147-225, 1985.
    • (1985) Comm. Pure Appl. Math , vol.24 , pp. 147-225
    • Varadhan, S.R.S.1    Williams, R.J.2
  • 48
    • 51249177074 scopus 로고
    • Reflected Brownian motion in a wedge: Semimartingale property
    • R. J. Williams. Reflected Brownian motion in a wedge: semimartingale property. Probab. Theor. And Rel. Fields, 69:161-176, 1985.
    • (1985) Probab. Theor. And Rel. Fields , vol.69 , pp. 161-176
    • Williams, R.J.1
  • 49
    • 85037875753 scopus 로고
    • Stochastic Networks, IMA Volumes in Mathematics and Its Applications, F. P. Kelly and R. J. Williams, editors
    • R. J. Williams. Semimartingale reflecting Brownian motions in an orthant. Stochastic Networks, IMA Volumes in Mathematics and Its Applications, F. P. Kelly and R. J. Williams, editors, 125-137, 1995.
    • (1995) Semimartingale Reflecting Brownian Motions in an Orthant , pp. 125-137
    • Williams, R.J.1


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