메뉴 건너뛰기




Volumn 36, Issue 6, 2008, Pages 2092-2125

Weak solutions for forward-backward SDES-A martingale problem approach

Author keywords

Forward backward stochastic differential equations; Martingale problems; Uniqueness; Viscosity solutions; Weak solutions

Indexed keywords


EID: 61849083018     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOP0383     Document Type: Article
Times cited : (25)

References (26)
  • 1
    • 0038521393 scopus 로고    scopus 로고
    • Weak solutions of forward-backward SDE's
    • MR 1978231
    • ANTONELLI, F. and MA, J. (2003). Weak solutions of forward-backward SDE's. Stochastic Anal. Appl. 21 493-514. MR 1978231
    • (2003) Stochastic Anal. Appl , vol.21 , pp. 493-514
    • ANTONELLI, F.1    MA, J.2
  • 4
    • 84856375785 scopus 로고    scopus 로고
    • On weak solutions of backward stochastic differential equations
    • MR2141331
    • BUCKDAHN, R., ENGELBERT, H.-J. and RǍ ŞCANU, A. (2004). On weak solutions of backward stochastic differential equations. Tear. Veroyatn. Primen. 49 70-108. MR2141331
    • (2004) Tear. Veroyatn. Primen , vol.49 , pp. 70-108
    • BUCKDAHN, R.1    ENGELBERT, H.-J.2    RǍ ŞCANU, A.3
  • 5
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • MR1118699
    • CRANDALL, M. G., ISHII, H. and LIONS, P.-L. (1992). User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27 1-67. MR1118699
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , pp. 1-67
    • CRANDALL, M.G.1    ISHII, H.2    LIONS, P.-L.3
  • 6
    • 0036233502 scopus 로고    scopus 로고
    • On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case
    • MR 1901154
    • DELARUE, F. (2002). On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case. Stochastic Process. Appl. 99 209-286. MR 1901154
    • (2002) Stochastic Process. Appl , vol.99 , pp. 209-286
    • DELARUE, F.1
  • 7
    • 61849129070 scopus 로고    scopus 로고
    • DELARUE, F. (2003). Estimates of the solutions of a system of quasi-linear PDEs. A probabilis-tic scheme. In Séminaire de Probabilites XXXVII. Lecture Notes in Math. 1832 290-332. Springer, Berlin. MR2053051
    • DELARUE, F. (2003). Estimates of the solutions of a system of quasi-linear PDEs. A probabilis-tic scheme. In Séminaire de Probabilites XXXVII. Lecture Notes in Math. 1832 290-332. Springer, Berlin. MR2053051
  • 8
    • 33750631031 scopus 로고    scopus 로고
    • DELARUE, F. and GUATTERI, G. (2006). Weak existence and uniqueness of FBSDEs. Stochastic Processes Appl. 116 1712-1742. MR2307056
    • DELARUE, F. and GUATTERI, G. (2006). Weak existence and uniqueness of FBSDEs. Stochastic Processes Appl. 116 1712-1742. MR2307056
  • 10
    • 0031542653 scopus 로고    scopus 로고
    • Backward stochastic differential equations in finance
    • MR 1434407
    • EL KAROUI, N., PENG, S. and QUENEZ, M. C. (1997). Backward stochastic differential equations in finance. Math. Finance 7 1-71. MR 1434407
    • (1997) Math. Finance , vol.7 , pp. 1-71
    • EL KAROUI, N.1    PENG, S.2    QUENEZ, M.C.3
  • 11
    • 61849127491 scopus 로고    scopus 로고
    • ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes. Characterization and Convergence. Wiley, New York. MR838085
    • ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes. Characterization and Convergence. Wiley, New York. MR838085
  • 12
    • 2542501546 scopus 로고    scopus 로고
    • Nonlinear Feynman-Kae formula and discrete-functional-type BSDEs with continuous coefficients
    • MR2062566
    • Hu, Y. and MA, J. (2004). Nonlinear Feynman-Kae formula and discrete-functional-type BSDEs with continuous coefficients. Stochastic Process. Appl. 112 23-51. MR2062566
    • (2004) Stochastic Process. Appl , vol.112 , pp. 23-51
    • Hu, Y.1    MA, J.2
  • 13
    • 61849137456 scopus 로고    scopus 로고
    • IKEDA, N. and WATANABE, S. (1989). Stochastic Differential Equations and Diffusion Processes, 2nd ed. North-Holland, Amsterdam. MR1011252
    • IKEDA, N. and WATANABE, S. (1989). Stochastic Differential Equations and Diffusion Processes, 2nd ed. North-Holland, Amsterdam. MR1011252
  • 14
    • 0034345576 scopus 로고    scopus 로고
    • Backward stochastic differential equations and partial differential equations with quadratic growth
    • MR 1782267
    • KOBYLANSKI, M. (2000). Backward stochastic differential equations and partial differential equations with quadratic growth. Ann. Probab. 28 558-602. MR 1782267
    • (2000) Ann. Probab , vol.28 , pp. 558-602
    • KOBYLANSKI, M.1
  • 15
    • 0031116187 scopus 로고    scopus 로고
    • Backward stochastic differential equations with continuous coefficient
    • MR 1602231
    • LEPELTIER, J. P. and SAN MARTIN, J. (1997). Backward stochastic differential equations with continuous coefficient. Statist. Probab. Lett. 32 425-430. MR 1602231
    • (1997) Statist. Probab. Lett , vol.32 , pp. 425-430
    • LEPELTIER, J.P.1    SAN MARTIN, J.2
  • 16
    • 0344891803 scopus 로고
    • Solving forward-backward stochastic differential equations explicitly-a four step scheme
    • MR1262970
    • MA, J., PROTTER, P. and YONG, J. M. (1994). Solving forward-backward stochastic differential equations explicitly-a four step scheme. Probab. Theory Related Fields 98 339-359. MR1262970
    • (1994) Probab. Theory Related Fields , vol.98 , pp. 339-359
    • MA, J.1    PROTTER, P.2    YONG, J.M.3
  • 17
    • 0000475954 scopus 로고
    • Solvability of forward-backward SDEs and the nodal set of Hamilton-Jacobi-Bellman equations
    • MR 1370779
    • MA, J. and YONG, J. (1995). Solvability of forward-backward SDEs and the nodal set of Hamilton-Jacobi-Bellman equations. Chinese Ann. Math. Ser. B 16 279-298. MR 1370779
    • (1995) Chinese Ann. Math. Ser. B , vol.16 , pp. 279-298
    • MA, J.1    YONG, J.2
  • 19
    • 0036439108 scopus 로고    scopus 로고
    • Representation theorems for backward stochastic differential equations
    • MR 1936598
    • MA, J. and ZHANG, J. (2002). Representation theorems for backward stochastic differential equations. Ann. Appl. Probab. 12 1390-1418. MR 1936598
    • (2002) Ann. Appl. Probab , vol.12 , pp. 1390-1418
    • MA, J.1    ZHANG, J.2
  • 20
    • 0036003097 scopus 로고    scopus 로고
    • Path regularity for solutions of backward stochastic differential equations
    • MR 1894066
    • MA, J. and ZHANG, J. (2002). Path regularity for solutions of backward stochastic differential equations. Probab. Theory Related Fields 122 163-190. MR 1894066
    • (2002) Probab. Theory Related Fields , vol.122 , pp. 163-190
    • MA, J.1    ZHANG, J.2
  • 21
    • 61849083860 scopus 로고    scopus 로고
    • Weak solutions of forward-backward SDEs and their uniqueness
    • Preprint
    • MA, J., ZHANG, J. and ZHENG, Z. (2005). Weak solutions of forward-backward SDEs and their uniqueness. Preprint.
    • (2005)
    • MA, J.1    ZHANG, J.2    ZHENG, Z.3
  • 22
    • 61849155488 scopus 로고    scopus 로고
    • MEYER, P.-A. and ZHENG, W. A. (1984). Tightness criteria for laws of semimartingales. Ann. Inst. H. Poincaré Probab. Statist. 20 353-372. MR771895
    • MEYER, P.-A. and ZHENG, W. A. (1984). Tightness criteria for laws of semimartingales. Ann. Inst. H. Poincaré Probab. Statist. 20 353-372. MR771895
  • 23
    • 0001680091 scopus 로고
    • Continuity of solutions of parabolic and elliptic equations
    • MR0100158
    • NASH, J. (1958). Continuity of solutions of parabolic and elliptic equations. Amer. J. Math. 80 931-954. MR0100158
    • (1958) Amer. J. Math , vol.80 , pp. 931-954
    • NASH, J.1
  • 24
    • 0025262967 scopus 로고
    • Adapted solution of a backward stochastic differential equation
    • MR1037747
    • PARDOUX, É. and PENG, S. G. (1990). Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 55-61. MR1037747
    • (1990) Systems Control Lett , vol.14 , pp. 55-61
    • PARDOUX, E.1    PENG, S.G.2
  • 26
    • 61849126063 scopus 로고    scopus 로고
    • STROOCK, D. W. and VARADHAN, S. R. S. (1979). Multidimensional Diffusion Processes. Springer, Berlin. MR532498
    • STROOCK, D. W. and VARADHAN, S. R. S. (1979). Multidimensional Diffusion Processes. Springer, Berlin. MR532498


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.