메뉴 건너뛰기




Volumn 49, Issue 1, 2005, Pages 16-50

On weak solutions of backward stochastic differential equations

Author keywords

Backward stochastic differential equation; Meyer Zheng topology; Pathwise uniqueness; Strong solution; Tsirelson's example; Uniqueness in law; Weak convergence; Weak solution

Indexed keywords


EID: 17544369795     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0040585X97980877     Document Type: Article
Times cited : (22)

References (33)
  • 1
    • 0038521393 scopus 로고    scopus 로고
    • Weak solutions of forward-backward SDE's
    • F. ANTONELLI AND J. MA, Weak solutions of forward-backward SDE's, Stochastic Anal. Appl., 21 (2003), pp. 493-514.
    • (2003) Stochastic Anal. Appl. , vol.21 , pp. 493-514
    • Antonelli, F.1    Ma, J.2
  • 2
    • 0039668287 scopus 로고
    • Necessary optimality conditions for stochastic differential equations
    • V. ARKIN AND M. SAKSONOV, Necessary optimality conditions for stochastic differential equations, Soviet Math. Dokl., 20 (1979), pp. 1-5.
    • (1979) Soviet Math. Dokl. , vol.20 , pp. 1-5
    • Arkin, V.1    Saksonov, M.2
  • 3
    • 0037715283 scopus 로고    scopus 로고
    • Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient
    • K. BAHLALI, E. H. ESSAKY, M. HASSANI, AND E. PARDOUX, Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient, C. R. Acad. Sci. Paris, 335 (2002), pp. 757-762.
    • (2002) C. R. Acad. Sci. Paris , vol.335 , pp. 757-762
    • Bahlali, K.1    Essaky, E.H.2    Hassani, M.3    Pardoux, E.4
  • 4
    • 0000929070 scopus 로고
    • Conjugate convex functions in optimal stochastic control
    • J. M. BISMUT, Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl., 44 (1973), pp. 384-404.
    • (1973) J. Math. Anal. Appl. , vol.44 , pp. 384-404
    • Bismut, J.M.1
  • 5
    • 0007791583 scopus 로고
    • Contrôle des systèmes linéaires quadratiques: Applications de l'intégrale stochastique
    • Séminaire de Probabilités XII, Springer-Verlag, Berlin
    • J. M. BISMUT, Contrôle des systèmes linéaires quadratiques: applications de l'intégrale stochastique, in Séminaire de Probabilités XII, Lecture Notes in Math. 649, Springer-Verlag, Berlin, 1978, pp. 180-264.
    • (1978) Lecture Notes in Math. , vol.649 , pp. 180-264
    • Bismut, J.M.1
  • 6
    • 84888926880 scopus 로고    scopus 로고
    • Isolated singular points of stochastic differential equations
    • Stochastic Processes and Related Topics, R. Buckdahn et al., eds., Taylor & Francis, London
    • A. S. CHERNY AND H.-J. ENGELBERT, Isolated singular points of stochastic differential equations, in Stochastic Processes and Related Topics, Proceedings of the 12th Winter School (Siegmundsburg) 2000, R. Buckdahn et al., eds., Taylor & Francis, London, 2002, pp. 55-80.
    • (2002) Proceedings of the 12th Winter School (Siegmundsburg) 2000 , pp. 55-80
    • Cherny, A.S.1    Engelbert, H.-J.2
  • 9
    • 0000217551 scopus 로고
    • On solutions of one-dimensional stochastic differential equations without drift
    • H.-J. ENGELBERT AND W. SCHMIDT, On solutions of one-dimensional stochastic differential equations without drift, Z. Wahrsch. Verw. Gebiete, 68 (1985), pp. 287-314.
    • (1985) Z. Wahrsch. Verw. Gebiete , vol.68 , pp. 287-314
    • Engelbert, H.-J.1    Schmidt, W.2
  • 10
    • 0000495184 scopus 로고
    • On one-dimensional stochastic differential equations with generalized drift
    • Stochastic Differential Equations, Springer-Verlag, Berlin
    • H.-J. ENGELBERT AND W. SCHMIDT, On one-dimensional stochastic differential equations with generalized drift, in Stochastic Differential Equations, Lecture Notes in Control and Inform. Sci. 69, Springer-Verlag, Berlin, 1985, pp. 143-155.
    • (1985) Lecture Notes in Control and Inform. Sci. , vol.69 , pp. 143-155
    • Engelbert, H.-J.1    Schmidt, W.2
  • 11
    • 84985321653 scopus 로고
    • Strong Markov continuous local martingales and solutions of one-dimensional stochastic differential equations
    • H.-J. ENGELBERT AND W. SCHMIDT, Strong Markov continuous local martingales and solutions of one-dimensional stochastic differential equations. I, II, III, Math. Nachr., 143 (1989), pp. 167-184; 144 (1989), pp. 241-281; 151 (1991), pp. 149-197.
    • (1989) I, II, III, Math. Nachr. , vol.143 , pp. 167-184
    • Engelbert, H.-J.1    Schmidt, W.2
  • 12
    • 84985425932 scopus 로고
    • H.-J. ENGELBERT AND W. SCHMIDT, Strong Markov continuous local martingales and solutions of one-dimensional stochastic differential equations. I, II, III, Math. Nachr., 143 (1989), pp. 167-184; 144 (1989), pp. 241-281; 151 (1991), pp. 149-197.
    • (1989) I, II, III, Math. Nachr. , vol.144 , pp. 241-281
  • 13
    • 84985383272 scopus 로고
    • H.-J. ENGELBERT AND W. SCHMIDT, Strong Markov continuous local martingales and solutions of one-dimensional stochastic differential equations. I, II, III, Math. Nachr., 143 (1989), pp. 167-184; 144 (1989), pp. 241-281; 151 (1991), pp. 149-197.
    • (1991) I, II, III, Math. Nachr. , vol.151 , pp. 149-197
  • 14
    • 1642360307 scopus 로고    scopus 로고
    • BSDEs with continuous coefficients and stochastic differential games
    • N. El Karoui et al., eds., Longman, Harlow
    • S. HAMADÉNE, J.-P. LEPELTIER, AND S. PENG, BSDEs with continuous coefficients and stochastic differential games, in Backward Stochastic Differential Equations, N. El Karoui et al., eds., Longman, Harlow, 1997, pp. 115-128.
    • (1997) Backward Stochastic Differential Equations , pp. 115-128
    • Hamadéne, S.1    Lepeltier, J.-P.2    Peng, S.3
  • 15
    • 0040361170 scopus 로고
    • Differential equations determining Markov processes
    • in Japanese
    • K. ITÔ, Differential equations determining Markov processes, Zenkoku Shijō Sūgaku Danwakai, 244 (1942), pp. 1352-1400 (in Japanese).
    • (1942) Zenkoku Shijō Sūgaku Danwakai , vol.244 , pp. 1352-1400
    • Itô, K.1
  • 16
    • 0001739440 scopus 로고
    • On stochastic differential equations
    • K. ITÔ, On stochastic differential equations, Mem. Amer. Math. Soc., 4 (1951), pp. 1-51.
    • (1951) Mem. Amer. Math. Soc. , vol.4 , pp. 1-51
    • Itô, K.1
  • 17
    • 0003353846 scopus 로고
    • Calcul stochastique et problèmes de martingales
    • Springer-Verlag, Berlin
    • J. JACOD, Calcul stochastique et problèmes de martingales, Lecture Notes in Math. 714, Springer-Verlag, Berlin, 1979.
    • (1979) Lecture Notes in Math. , vol.714
    • Jacod, J.1
  • 18
    • 17544373673 scopus 로고
    • On the pontryagin maximum principle for the linear stochastic differential equations
    • CEMI, Moscow, (in Russian)
    • YU. KABANOV, On the Pontryagin Maximum Principle for the Linear Stochastic Differential Equations, Probabilistic Models and Control of Economical Processes, CEMI, Moscow, 1978 (in Russian).
    • (1978) Probabilistic Models and Control of Economical Processes
    • Kabanov, Yu.1
  • 19
    • 0000307874 scopus 로고
    • On itô's stochastic integral equations
    • N. V. KRYLOV, On Itô's stochastic integral equations, Theory Probab. Appl., 14 (1969) pp. 330-338.
    • (1969) Theory Probab. Appl. , vol.14 , pp. 330-338
    • Krylov, N.V.1
  • 21
    • 0031116187 scopus 로고    scopus 로고
    • Backward stochastic differential equations with continuous coefficient
    • J.-P. LEPELTIER AND J. SAN MARTIN, Backward stochastic differential equations with continuous coefficient, Statist. Probab. Lett., 32 (1997), pp. 425-430.
    • (1997) Statist. Probab. Lett. , vol.32 , pp. 425-430
    • Lepeltier, J.-P.1    San Martin, J.2
  • 23
    • 0025262967 scopus 로고
    • Adapted solution of a backward stochastic differential equation
    • E. PARDOUX AND S. PENG, Adapted solution of a backward stochastic differential equation, Systems Control Lett., 14 (1990), pp. 55-61.
    • (1990) Systems Control Lett. , vol.14 , pp. 55-61
    • Pardoux, E.1    Peng, S.2
  • 26
    • 0001512971 scopus 로고
    • On existence and stability of weak solutions of multidimensional stochastic differential equations with measurable coefficients
    • A. ROZKOSZ AND L. SLOMIŃSKI, On existence and stability of weak solutions of multidimensional stochastic differential equations with measurable coefficients, Stochastic Process. Appl., 37 (1991), pp. 187-197.
    • (1991) Stochastic Process. Appl. , vol.37 , pp. 187-197
    • Rozkosz, A.1    Slomiński, L.2
  • 27
    • 0031575038 scopus 로고    scopus 로고
    • On stability and existence of SDEs with reflection at the boundary
    • A. ROZKOSZ AND L. SLOMIŃSKI, On stability and existence of SDEs with reflection at the boundary, Stochastic Process. Appl., 68 (1997), pp. 285-302.
    • (1997) Stochastic Process. Appl. , vol.68 , pp. 285-302
    • Rozkosz, A.1    Slomiński, L.2
  • 29
    • 0001379748 scopus 로고
    • Stochastic equations for diffusion processes in a bounded region
    • A. V. SKOROKHOD, Stochastic equations for diffusion processes in a bounded region. I, II, Theory Probab. Appl., 6 (1961) pp. 264-274; 7 (1962), pp. 3-23.
    • (1961) I, II, Theory Probab. Appl. , vol.6 , pp. 264-274
    • Skorokhod, A.V.1
  • 30
    • 84888921774 scopus 로고
    • A. V. SKOROKHOD, Stochastic equations for diffusion processes in a bounded region. I, II, Theory Probab. Appl., 6 (1961) pp. 264-274; 7 (1962), pp. 3-23.
    • (1962) I, II, Theory Probab. Appl. , vol.7 , pp. 3-23
  • 31
    • 0041148536 scopus 로고
    • An example of a stochastic differential equation having no strong solution
    • B. TSIREL'SON, An example of a stochastic differential equation having no strong solution, Theory Probab. Appl., 20 (1975), pp. 416-418.
    • (1975) Theory Probab. Appl. , vol.20 , pp. 416-418
    • Tsirel'son, B.1
  • 32
    • 0000827166 scopus 로고
    • On the uniqueness of solutions of stochastic differential equations
    • T. YAMADA AND S. WATANABE, On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ., 11 (1971), pp. 155-167.
    • (1971) J. Math. Kyoto Univ. , vol.11 , pp. 155-167
    • Yamada, T.1    Watanabe, S.2
  • 33
    • 84957165179 scopus 로고
    • A transformation of the phase space of a process that removes the drift
    • A. K. ZVONKIN, A transformation of the phase space of a process that removes the drift, Math. USSR Sb., 2 (1974), pp. 129-149.
    • (1974) Math. USSR Sb. , vol.2 , pp. 129-149
    • Zvonkin, A.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.