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Volumn 25, Issue 3, 1997, Pages 1135-1159

Backwards SDE with random terminal time and applications to semilinear elliptic PDE

Author keywords

Brownian motion; Monotonicity; Semilinear elliptic PDE; Stochastic differential equation; Stopping time; Viscosity solution

Indexed keywords


EID: 0031511874     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1024404508     Document Type: Article
Times cited : (162)

References (11)
  • 1
    • 0002508109 scopus 로고    scopus 로고
    • Backward stochastic differential equations and integral-partial differential equations
    • BARLES, G., BUCKDAHN, R. and PARDOUX, E. (1997). Backward stochastic differential equations and integral-partial differential equations. Stochastics Stochastics Rep. 60 57-83.
    • (1997) Stochastics Stochastics Rep. , vol.60 , pp. 57-83
    • Barles, G.1    Buckdahn, R.2    Pardoux, E.3
  • 2
    • 84963420752 scopus 로고
    • The dirichlet problem for semilinear second-order degenerate elliptic equations and applications to stochastic exit time control problems
    • BARLES, G. and BURDEAU, J. (1995). The Dirichlet problem for semilinear second-order degenerate elliptic equations and applications to stochastic exit time control problems. Comm. Partial Differential Equations 20 129-178.
    • (1995) Comm. Partial Differential Equations , vol.20 , pp. 129-178
    • Barles, G.1    Burdeau, J.2
  • 3
    • 0010805570 scopus 로고
    • Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions
    • BARLES, G. and MURAT, F. (1995). Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions. Arch. Rational Mech. Anal. 133 77-101.
    • (1995) Arch. Rational Mech. Anal. , vol.133 , pp. 77-101
    • Barles, G.1    Murat, F.2
  • 4
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • CRANDALL, M., ISHII, H. and LIONS, P. L. (1992). User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 1-67.
    • (1992) Bull. Amer. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.1    Ishii, H.2    Lions, P.L.3
  • 5
    • 0005275458 scopus 로고
    • Constructing gamma-martingales with prescribed limit using backwards SDE
    • DARLING, R. W. R. (1995). Constructing gamma-martingales with prescribed limit using backwards SDE. Ann. Probab. 23 1234-1261.
    • (1995) Ann. Probab. , vol.23 , pp. 1234-1261
    • Darling, R.W.R.1
  • 6
    • 0025262967 scopus 로고
    • Adapted solution of a backward stochastic differential equation
    • PARDOUX, E. and PENG, S. (1990). Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 55-61.
    • (1990) Systems Control Lett. , vol.14 , pp. 55-61
    • Pardoux, E.1    Peng, S.2
  • 8
    • 0040050366 scopus 로고
    • Probabilistic interpretation for a system of nonlinear parabolic partial differential equations
    • To appear
    • PARDOUX, E., PRADEILLES, F. and RAO, Z. (1995). Probabilistic interpretation for a system of nonlinear parabolic partial differential equations. Ann. Inst. H. Poincaré Probab. Statist. To appear.
    • (1995) Ann. Inst. H. Poincaré Probab. Statist.
    • Pardoux, E.1    Pradeilles, F.2    Rao, Z.3
  • 9
    • 0002686129 scopus 로고
    • Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
    • PENG, S. (1991). Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. Stochastics Stochastics Rep. 37 61-74.
    • (1991) Stochastics Stochastics Rep. , vol.37 , pp. 61-74
    • Peng, S.1
  • 11
    • 0001391656 scopus 로고
    • On degenerate elliptic-parabolic operators of second order and their associated diffusions
    • STROOCK, D. W. and VARADHAN, S. R. S. (1972). On degenerate elliptic-parabolic operators of second order and their associated diffusions. Comm. Pure Appl. Math. 25 651-713.
    • (1972) Comm. Pure Appl. Math. , vol.25 , pp. 651-713
    • Stroock, D.W.1    Varadhan, S.R.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.