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This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in (y, z) non-uniformly with respect to t. By establishing some results on deterministic backward differential equations with general time intervals, and by virtue of Girsanov’s theorem and convolution technique, we prove a new existence and uniqueness result for solutions of this kind of backward stochastic differential equations, which extends the results of [8] and [6] to the general time interval case.
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참고문헌 (13)
참고문헌 신청
E. Pardoux / 1990 / Adapted solution of a backward stochastic differential equation / Systems Control Lett 14 (1) : 55 ~ 61
J.-P. Lepeltier / 1997 / Backward stochastic differential equations with con-tinuous coefficient / Statist. Probab. Lett 32 (4) : 425 ~ 430
K. Bahlali / 2001 / Backward stochastic differential equations with locally Lipschitz coefficient / C. R. Math. Acad. Sci. Paris 333 (5) : 481 ~ 486
M. Kobylanski / 2000 / Backward stochastic differential equations and partial differential equa-tions with quadratic growth / Ann. Probab 28 (2) : 558 ~ 602
N. El Karoui / 1997 / Backward stochastic differential equations in finance / Math. Finance 7 (1) : 1 ~ 71
J.-P. Lepeltier / 1997 / Backward stochastic differential equations with con-tinuous coefficient / Statist. Probab. Lett 32 (4) : 425 ~ 430
K. Bahlali / 2001 / Backward stochastic differential equations with locally Lipschitz coefficient / C. R. Math. Acad. Sci. Paris 333 (5) : 481 ~ 486
M. Kobylanski / 2000 / Backward stochastic differential equations and partial differential equa-tions with quadratic growth / Ann. Probab 28 (2) : 558 ~ 602
N. El Karoui / 1997 / Backward stochastic differential equations in finance / Math. Finance 7 (1) : 1 ~ 71
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