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Volumn 94, Issue 2, 2001, Pages 317-337

Euler's approximations of solutions of SDEs with reflecting boundary

Author keywords

Penalization scheme; Projection scheme; Reflecting boundary condition; Skorokhod problem; Stochastic differential equation

Indexed keywords


EID: 18044404434     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(01)00087-4     Document Type: Article
Times cited : (78)

References (25)
  • 1
    • 0000044071 scopus 로고
    • Stopping time and tightness
    • Aldous D.J. Stopping time and tightness. Ann. Probab. 6:1978;335-340.
    • (1978) Ann. Probab. , vol.6 , pp. 335-340
    • Aldous, D.J.1
  • 2
    • 0000556895 scopus 로고
    • Diffusional approximation for processes with a normal reflection
    • Anulova S.V., Liptzer R.Sh. Diffusional approximation for processes with a normal reflection. Theory Probab. Appl. 35:1990;417-431.
    • (1990) Theory Probab. Appl. , vol.35 , pp. 417-431
    • Anulova, S.V.1    Liptzer, R.sh.2
  • 3
    • 0019689061 scopus 로고
    • Strong solutions of stochastic differential equations with boundary conditions
    • Chitashvili R.J., Lazrieva N.L. Strong solutions of stochastic differential equations with boundary conditions. Stochastics. 5:1981;225-309.
    • (1981) Stochastics , vol.5 , pp. 225-309
    • Chitashvili, R.J.1    Lazrieva, N.L.2
  • 5
    • 0001985427 scopus 로고
    • On lipschitz continuity of the solution mapping to the Skorokhod problem, with applications
    • Dupuis P., Ishii H. On lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Stochastics Stochastics Rep. 35:1991;31-62.
    • (1991) Stochastics Stochastics Rep. , vol.35 , pp. 31-62
    • Dupuis, P.1    Ishii, H.2
  • 6
    • 0001045192 scopus 로고
    • SDEs with oblique reflection on nonsmooth domain
    • Dupuis P., Ishii H. SDEs with oblique reflection on nonsmooth domain. Ann. Probab. 21(1):1993;554-580.
    • (1993) Ann. Probab. , vol.21 , Issue.1 , pp. 554-580
    • Dupuis, P.1    Ishii, H.2
  • 7
    • 0040361064 scopus 로고    scopus 로고
    • Existence of strong solution for Itô's stochastic equations via approximations
    • Gyöngy I., Krylov N. Existence of strong solution for Itô's stochastic equations via approximations. Probab. Theory Related Fields. 105:1996;143-158.
    • (1996) Probab. Theory Related Fields , vol.105 , pp. 143-158
    • Gyöngy, I.1    Krylov, N.2
  • 10
    • 0000367265 scopus 로고
    • Weak limit theorems for stochastic integrals and stochastic differential equations
    • Kurtz T.G., Protter P. Weak limit theorems for stochastic integrals and stochastic differential equations. Ann. Probab. 19:1991;1035-1070.
    • (1991) Ann. Probab. , vol.19 , pp. 1035-1070
    • Kurtz, T.G.1    Protter, P.2
  • 11
    • 84990576543 scopus 로고
    • Stochastic differential equations with reflecting boundary conditions
    • Lions P.L., Sznitman A.S. Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. XXXVII:1984;511-537.
    • (1984) Comm. Pure Appl. Math. , vol.37 , pp. 511-537
    • Lions, P.L.1    Sznitman, A.S.2
  • 13
    • 0039075424 scopus 로고
    • Stochastic variational inequality for reflected diffusion
    • Menaldi J.L. Stochastic variational inequality for reflected diffusion. Indiana Univ. Math. J. 32:1983;733-744.
    • (1983) Indiana Univ. Math. J. , vol.32 , pp. 733-744
    • Menaldi, J.L.1
  • 14
    • 0042044133 scopus 로고
    • Approximations for stochastic differential equation with reflecting convex boundaries
    • Pettersson R. Approximations for stochastic differential equation with reflecting convex boundaries. Stochastic Process. Appl. 59:1995;295-308.
    • (1995) Stochastic Process. Appl. , vol.59 , pp. 295-308
    • Pettersson, R.1
  • 15
    • 0041568068 scopus 로고    scopus 로고
    • Penalization schemes for reflecting stochastic differential equations
    • Pettersson R. Penalization schemes for reflecting stochastic differential equations. Bernoulli. 3(4):1997;403-414.
    • (1997) Bernoulli , vol.3 , Issue.4 , pp. 403-414
    • Pettersson, R.1
  • 16
  • 17
    • 0000605830 scopus 로고
    • Stochastic differential equations for multi-dimensional domain with reflecting boundary
    • Saisho Y. Stochastic differential equations for multi-dimensional domain with reflecting boundary. Probab. Theory Related Fields. 74:1987;455-477.
    • (1987) Probab. Theory Related Fields , vol.74 , pp. 455-477
    • Saisho, Y.1
  • 18
    • 0001379748 scopus 로고
    • Stochastic equations for diffusion processes in a bounded region 1
    • Skorokhod A.V. Stochastic equations for diffusion processes in a bounded region 1. Theory Probab. Appl. 6:1961;264-274.
    • (1961) Theory Probab. Appl. , vol.6 , pp. 264-274
    • Skorokhod, A.V.1
  • 19
    • 38249023375 scopus 로고
    • Stability of strong solutions of stochastic differential equations
    • Slomiński L. Stability of strong solutions of stochastic differential equations. Stochastic Process. Appl. 31:1989;173-202.
    • (1989) Stochastic Process. Appl. , vol.31 , pp. 173-202
    • Slomiński, L.1
  • 20
    • 0040259240 scopus 로고
    • On approximation of solutions of multidimensional SDEs with reflecting boundary conditions
    • Slomiński L. On approximation of solutions of multidimensional SDEs with reflecting boundary conditions. Stochastic Process. Appl. 50:1994;197-219.
    • (1994) Stochastic Process. Appl. , vol.50 , pp. 197-219
    • Slomiński, L.1
  • 21
    • 0011704065 scopus 로고    scopus 로고
    • Stability of stochastic differential equations driven by general semimartingales
    • Slomiński L. Stability of stochastic differential equations driven by general semimartingales. Diss. Math. CCCXLIX:1996;1-113.
    • (1996) Diss. Math. , vol.349 , pp. 1-113
    • Slomiński, L.1
  • 22
    • 0008990982 scopus 로고
    • Stochastic differential equations with convex constraint
    • Storm A. Stochastic differential equations with convex constraint. Stochastics Stochastics Rep. 53:1995;241-274.
    • (1995) Stochastics Stochastics Rep. , vol.53 , pp. 241-274
    • Storm, A.1
  • 23
    • 0013530573 scopus 로고
    • Loi de semimartingales et critères de compacité
    • Springer, Berlin, Heidelberg, New York
    • Stricker, C., 1985. Loi de semimartingales et critères de compacité, Sém. de Probab. XIX Lecture Notes in Mathematics, 209-217. 1123 Springer, Berlin, Heidelberg, New York.
    • (1985) Sém. de Probab. XIX Lecture Notes in Mathematics , vol.209-217 , pp. 1123
    • Stricker, C.1
  • 24
    • 84972526612 scopus 로고
    • Stochastic differential equations with reflecting boundary condition in convex regions
    • Tanaka H. Stochastic differential equations with reflecting boundary condition in convex regions. Hiroshima Math. J. 9:1979;163-177.
    • (1979) Hiroshima Math. J. , vol.9 , pp. 163-177
    • Tanaka, H.1
  • 25
    • 0040654610 scopus 로고
    • Remark of rate of convergence in the invariance principle
    • Utev S.A. Remark of rate of convergence in the invariance principle. (Russian) Sibirs. Mat. Zh. 22:1981;206-209.
    • (1981) (Russian) Sibirs. Mat. Zh. , vol.22 , pp. 206-209
    • Utev, S.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.