Multidimensional BSDEs with weak monotonicity and general growth generators
Multidimensional BSDEs with weak monotonicity and general growth generators
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DOI：
10.1007/s10114-013-2128-x
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发表时间：
2013-03
期刊：
影响因子：
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通讯作者：
Shengjun Fan;Long Jiang
中科院分区：
文献类型：
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作者：
Shengjun Fan;Long Jiang
本文研究了一类生成元满足弱单调条件和一般增长条件的多维倒向随机微分方程。我们首先系统地利用先验估计、卷积方法、迭代、截断和Bihari不等式等技巧，建立了这类倒向随机微分方程解的存在唯一性结果。然后，我们综述了文献中与单调性条件密切相关的一些假设，并对它们进行了有效的比较，得到了我们的存在唯一性结果真正地把MAO条件和单调性条件与一般的增长条件统一起来，推广了一些已有的结果。最后，我们证明了这类倒向随机微分方程的稳定性定理和比较定理，改进了已有的一些结果。
This paper aims at solving a multidimensional backward stochastic differential equation (BSDE) whose generatorgsatisfies a weak monotonicity condition and a general growth condition iny. We first establish an existence and uniqueness result of solutions for this kind of BSDEs by using systematically the technique of the priori estimation, the convolution approach, the iteration, the truncation and the Bihari inequality. Then, we overview some assumptions related closely to the monotonicity condition in the literature and compare them in an effective way, which yields that our existence and uniqueness result really and truly unifies the Mao condition inyand the monotonicity condition with the general growth condition iny, and it generalizes some known results. Finally, we prove a stability theorem and a comparison theorem for this kind of BSDEs, which also improves some known results.