On existence, uniqueness and stability of solutions of multidimensional SDE's with reflecting boundary conditions
Słomínski, Leszek
Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993), p. 163-198 / Harvested from Numdam
Publié le : 1993-01-01
@article{AIHPB_1993__29_2_163_0,
     author = {S\l ominski, Leszek},
     title = {On existence, uniqueness and stability of solutions of multidimensional SDE's with reflecting boundary conditions},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {29},
     year = {1993},
     pages = {163-198},
     zbl = {0773.60055},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1993__29_2_163_0}
}
Słomínski, Leszek. On existence, uniqueness and stability of solutions of multidimensional SDE's with reflecting boundary conditions. Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993) pp. 163-198. http://gdmltest.u-ga.fr/item/AIHPB_1993__29_2_163_0/

[1] D.J. Aldous, Stopping Time and Tightness. II, Ann. Probab., Vol. 17, 1989, pp. 586- 595. | MR 985380 | Zbl 0686.60036

[2] S.V. Anulova and R.Sh. Liptzer, Diffusional Approximation for Processes with a Normal Reflection, Theory Probab. Appl., Vol. 35, 1990, pp.417-431. | MR 1069129 | Zbl 0735.60078

[3] P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968. | MR 233396 | Zbl 0172.21201

[4] M. Chaleyat-Maurel, N. El Karoui and B. Marchal, Réflexion discontinue et systèmes stochastiques, Ann. Probab., Vol. 8, 1980, pp. 1049-1067. | MR 602379 | Zbl 0448.60043

[5] C. Dellacherie and P.A. Meyer, Probabilités et Potentiel, Hermann, Paris, 1980. | MR 488194

[6] N. El Karoui and M. Chaleyat-Maurel, Un problème de réflexions au temps local et aux équations différentielles stochastiques sur R. Cas continu, Astérisque, Vol. 52- 53, 1978, pp.117-144.

[7] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981. | MR 637061 | Zbl 0495.60005

[8] J. Jacod and A.N. Shiryayev, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin, 1987. | MR 959133 | Zbl 0635.60021

[9] A. Jakubowski, J. Mémin and G. Pages, Convergence en loi des suites d'intégrales stochastiques sur l'espace D1 de Skorokhod, Probab. Th. Rel. Fields, Vol. 81, 1989, pp. 111-137. | MR 981569 | Zbl 0638.60049

[10] T.G. Kurtz and P. Protter, Weak Limit Theorems for Stochastic Integrals and Stochastic differential Equations, Ann. Probab., Vol. 19, 1991, pp. 1035-1070. | MR 1112406 | Zbl 0742.60053

[11] P.L. Lions and A.S. Sznitman, Stochastic Differential Equations with Reflecting Boundary Conditions, Communications on Pure and Applied Mathematics, Vol. 37, 1981, pp. 511-537. | MR 745330 | Zbl 0598.60060

[12] V. Mackievicius, SJP Stability of Symmetric Stochastic Differential Equations with Discontinuous Driving Semimartingales, Ann. Inst. Henri Poincaré, Vol. B23, 1987, pp. 575-592. | Numdam | Zbl 0636.60057

[13] H.P. Mckean, A Skorokhod's Integral Equations for a Reflecting Barrier Diffusion, J. Math. Kyoto Univ., Vol. 3, 1963, pp. 86-88. | Zbl 0202.46601

[14] J. Mémin and L. Słomiński, Condition UT et stabilité en loi des solutions d'équations différentielles stochastiques, Sém. de Probab. XXV, Lect. Notes in Math., No. 1485, Springer-Verlag, Berlin, Heidelberg, New York, 1991, pp. 162-177. | Numdam | MR 1187779 | Zbl 0746.60063

[15] M. Métivier and J. Pellaumail, Une formule de majoration pour martingales, C. R. Acad. Sci. Paris, T. 285, Series A, 1977, pp. 685-688. | MR 461651 | Zbl 0368.60057

[16] M. Métivier and J. Pellaumail, On a Stopped Doob's Inequality and General Stochastic Equations, Ann. Probab., Vol. 8, 1980, pp. 96-114. | MR 556417 | Zbl 0426.60059

[17] P.A. Meyer and W.A. Zheng, Tightness Criteria for Laws of Semimartingales, Ann. Inst. Henri Poincaré, Vol. B20, 1984, pp. 353-372. | Numdam | MR 771895 | Zbl 0551.60046

[18] P.A. Meyer, Note sur les martingales d'Azema, Sém. de Probab. XXIII, Lect. Notes in Math., Springer-Verlag, Berlin, Heidelberg, New York, 1989.

[19] P. Protter, Stochastic Differential Equations with Jump Reflection at the Boundary, Stochastics, Vol. 3, 1980, pp. 193-201. | MR 573203 | Zbl 0429.60057

[20] Y. Saisho, Stochastic Differential Equations for Multi-dimensional Domain with Reflecting Boundary, Probab. Th. Rel. Fields, Vol. 74, 1987, pp. 455-477. | MR 873889 | Zbl 0591.60049

[21] M.A. Shashiashvili, On the Variation of the Difference of Singular Components in the Skorokhod Problem and on Stochastic Differential Systems in a Half-Space, Stochastics, Vol. 24, 1988, pp. 151-169. | MR 972473 | Zbl 0648.60055

[22] A.V. Skorokhod, Stochastic Equations for Diffusion Processes in a Bounded Region 1, 2, Theory Probab. Appl., Vol. 6, 1961, pp. 264-274, Vol. 7, 1962, pp. 3-23. | Zbl 0215.53501

[23] L. Słomiński, Stability of Strong Solutions of Stochastic Differential Equations, Stoch. Processes Appl., Vol. 31, 1989, pp. 173-202. | MR 998112 | Zbl 0673.60065

[24] C. Stricker, Loi de semimartingales et critères de compacité, Sém. de Probab. XIX, Lect. Notes in Math., No. 1123, Springer-Verlag, Berlin, Heidelberg, New York, 1985. | Numdam | MR 889478 | Zbl 0558.60005

[25] H. Tanaka, Stochastic Differential Equations with Reflecting Boundary Condition in Convex Regions, Hiroshima Math. J., Vol. 9, 1979, pp. 163-177. | MR 529332 | Zbl 0423.60055

[26] S. Watanabe, On Stochastic Differential Equations for Multi-Dimensional Diffusion Processes with Boundary Conditions, J. Math. Kyoto Univ., Vol. 11, 1971, pp. 169- 180. | MR 275537 | Zbl 0212.20203