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Lishun, Xiao,Shengjun, Fan Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.2
The objective of this paper is solving multidimensional backward stochastic differential equations with general time intervals, in L<sup>p</sup> (p ≥ 1) sense, where the generator g satisfies a time-varying Osgood condition in y, a time-varying quasi-Hölder continuity condition in z, and its ith component depends on the ith row of z. Our result strengthens some existing works even for the case of finite time intervals.
MULTIDIMENSIONAL BSDES WITH UNIFORMLY CONTINUOUS GENERATORS AND GENERAL TIME INTERVALS
Fan, Shengjun,Wang, Yanbin,Xiao, Lishun Korean Mathematical Society 2015 대한수학회보 Vol.52 No.2
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.
MULTIDIMENSIONAL BSDES WITH UNIFORMLY CONTINUOUS GENERATORS AND GENERAL TIME INTERVALS
Shengjun Fan,Yanbin Wang,Lishun Xiao 대한수학회 2015 대한수학회보 Vol.52 No.2
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.