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This paper is devoted to the existence and uniqueness of $L^p\,(p>1)$ solutions for general time interval multidimensional backward stochastic differential equations (BSDEs for short), where the generator $g$ satisfies a $(p\wedge 2)$-order weak monotonicity condition in $y$ and a Lipschitz continuity condition in $z$, both non-uniformly in $t$. The corresponding stability theorem and comparison theorem are also proved.
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참고문헌 (20)
참고문헌 신청
C. Bender / 2000 / BSDEs with stochastic Lipschitz condition
P. Briand / 2003 / $L^p$ solutions of backward stochastic differential equations / Stochastic Process. Appl. 108(1):109~129
P. Briand / 2013 / A simple constructive approach to quadratic BSDEs with or without delay / Stochastic Process. Appl. 123(8):2921~2939
P. Briand / 2008 / Quadratic BSDEs with convex generators and unbounded terminal conditions / Probab. Theory Related Fields 141(3-4):543~567
Z. J. Chen / 1997 / Existence of solutions to backward stochastic differential equations with stopping times / Kexue Tongbao (Chinese) 42(22):2379~2382
P. Briand / 2003 /
P. Briand / 2013 / A simple constructive approach to quadratic BSDEs with or without delay / Stochastic Process. Appl. 123(8):2921~2939
P. Briand / 2008 / Quadratic BSDEs with convex generators and unbounded terminal conditions / Probab. Theory Related Fields 141(3-4):543~567
Z. J. Chen / 1997 / Existence of solutions to backward stochastic differential equations with stopping times / Kexue Tongbao (Chinese) 42(22):2379~2382
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