메뉴 건너뛰기




Volumn 114, Issue 2, 1999, Pages 123-150

Forward-backward stochastic differential equations and quasilinear parabolic PDEs

Author keywords

Backward stochastic differential equation; Contraction mapping theorem; Forward; Quasilinear parabolic partial differential equation

Indexed keywords


EID: 0033463544     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004409970001     Document Type: Article
Times cited : (309)

References (22)
  • 1
    • 0000580597 scopus 로고
    • Backward-forward stochastic differential equations
    • Antonelli, F.: Backward-forward stochastic differential equations, Ann. Appl. Probab. 3, pp. 777-793 (1993)
    • (1993) Ann. Appl. Probab. , vol.3 , pp. 777-793
    • Antonelli, F.1
  • 4
    • 84967708673 scopus 로고
    • User's guide to viscosity solution of second order partial differential equations
    • Crandall, M., Ishii, H., Lions, P.L.: User's guide to viscosity solution of second order partial differential equations, Bull. Amer. Math. Soc. 27, 1-67 (1992)
    • (1992) Bull. Amer. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.1    Ishii, H.2    Lions, P.L.3
  • 5
    • 0031511874 scopus 로고    scopus 로고
    • Backwards SDE with random terminal time, and applications to semilinear elliptic PDE
    • Darling, R.W.R., Pardoux, E.: Backwards SDE with Random Terminal Time, and Applications to Semilinear Elliptic PDE, Ann. Probab. 25, 1135-1159 (1997)
    • (1997) Ann. Probab. , vol.25 , pp. 1135-1159
    • Darling, R.W.R.1    Pardoux, E.2
  • 7
    • 0031542653 scopus 로고    scopus 로고
    • Backward stochastic differential equations in finance
    • El Karoui, N., Peng, S., Quenez, M.C.: Backward stochastic differential equations in finance, Math. Finance, 7, pp. 1-71 (1997)
    • (1997) Math. Finance , vol.7 , pp. 1-71
    • El Karoui, N.1    Peng, S.2    Quenez, M.C.3
  • 8
    • 0000036188 scopus 로고    scopus 로고
    • Sur la méthode de Picard (EDO et EDS)
    • Séminaire de Probabilités XXI
    • Denis Feyel: Sur la méthode de Picard (EDO et EDS), in Séminaire de Probabilités XXI, Lecture Notes in Mathematics 1247, pp. 515-519
    • Lecture Notes in Mathematics , vol.1247 , pp. 515-519
    • Feyel, D.1
  • 10
    • 51249168165 scopus 로고
    • Solution of forward-backward stochastic differential equations
    • Hu, Y., Peng, S.: Solution of forward-backward stochastic differential equations, Probab. Theory Relat. Fields 103, pp. 273-283 (1995)
    • (1995) Probab. Theory Relat. Fields , vol.103 , pp. 273-283
    • Hu, Y.1    Peng, S.2
  • 11
    • 0344891803 scopus 로고
    • Solving forward-backward stochastic differential equations explicitly- A four step scheme
    • Ma, J., Protter, P., Yong, J.: Solving forward-backward stochastic differential equations explicitly- a four step scheme, Probab. Theory Relat. Fields 98, pp. 339-359 (1994)
    • (1994) Probab. Theory Relat. Fields , vol.98 , pp. 339-359
    • Ma, J.1    Protter, P.2    Yong, J.3
  • 12
    • 0000475954 scopus 로고
    • Solvability of forward-backward SDE's and the nodal set of Hamilton-Jacobi-Bellman equations
    • Ma, J., Yong, J.: Solvability of forward-backward SDE's and the nodal set of Hamilton-Jacobi-Bellman equations, Chin. Ann. Math. 16B, pp. 279-298 (1995)
    • (1995) Chin. Ann. Math. , vol.16 B , pp. 279-298
    • Ma, J.1    Yong, J.2
  • 13
    • 0038434600 scopus 로고    scopus 로고
    • Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order
    • 1996, L. Decreusefond, J. Gjerde, B. Oksendal, A.S. Üstünel eds., Birkhäuser
    • Pardoux, E.: Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order, in Stochastic Analysis and Related Topics VI: The Geilo Workshop, 1996, L. Decreusefond, J. Gjerde, B. Oksendal, A.S. Üstünel eds., Birkhäuser, 79-127, 1998
    • (1998) Stochastic Analysis and Related Topics VI: The Geilo Workshop , vol.6 , pp. 79-127
    • Pardoux, E.1
  • 15
    • 0000268709 scopus 로고
    • Backward stochastic differential equations and quasi-linear parabolic partial differential equations
    • Rozovskii, B. L. Sowers, R. S. (eds.) Stochastic partial differential equations and their applications, Springer, Berlin, Heidelberg, New York
    • Pardoux, E., Peng, S.: Backward stochastic differential equations and quasi-linear parabolic partial differential equations, in Rozovskii, B. L. Sowers, R. S. (eds.) Stochastic partial differential equations and their applications, Lect. Notes in Control & Info. Sci. 176, Springer, Berlin, Heidelberg, New York 1992, pp. 200-217
    • (1992) Lect. Notes in Control & Info. Sci. , vol.176 , pp. 200-217
    • Pardoux, E.1    Peng, S.2
  • 17
    • 0002686129 scopus 로고
    • Probabilistic interpretation for systems of semilinear parabolic PDEs
    • Peng, S.: Probabilistic interpretation for systems of semilinear parabolic PDEs, Stochastics & Stochastic Reports 37, pp. 61-74 (1991)
    • (1991) Stochastics & Stochastic Reports , vol.37 , pp. 61-74
    • Peng, S.1
  • 18
    • 0001098095 scopus 로고
    • A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation
    • Peng, S.: A Generalized Dynamic Programming Principle and Hamilton-Jacobi-Bellman Equation, Stochastics & Stochastic Reports 38, pp. 119-134 (1992)
    • (1992) Stochastics & Stochastic Reports , vol.38 , pp. 119-134
    • Peng, S.1
  • 20
    • 0028500888 scopus 로고
    • Necessary conditions for optimal control of stochastic systems with random jumps
    • Tang, S., Li, X.: Necessary conditions for optimal control of stochastic systems with random jumps, SIAM J. Control and Optimization 32, pp. 1447-1475 (1994)
    • (1994) SIAM J. Control and Optimization , vol.32 , pp. 1447-1475
    • Tang, S.1    Li, X.2
  • 22
    • 0041022466 scopus 로고    scopus 로고
    • Finding adapted solution of forward-backward stochastic differential equations - Method of continuation
    • Yong, J.: Finding Adapted Solution of Forward-Backward Stochastic Differential Equations - Method of Continuation, Probab. Theory and Rel. Fields 107, 537-572 (1997)
    • (1997) Probab. Theory and Rel. Fields , vol.107 , pp. 537-572
    • Yong, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.