In this paper,we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in the second unknown z.Using a linearization technique and the BMO martingale theory,we fi...In this paper,we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in the second unknown z.Using a linearization technique and the BMO martingale theory,we first apply a fixed-point argument to establish the uniqueness and existence result for the case with bounded terminal condition and obstacle.Then,with the help of theθ-method,we develop a successive approximation procedure to remove the boundedness condition on the terminal condition and obstacle when the generator is concave(or convex)with respect to the second unknown.展开更多
给出了FMP的三I解的一般形式 ,证明了关于区间值模糊推理的单调性定理、下确界定理以及存在性定理 .在分析了规则后件相对于前件的敏感性的基础上提出了 p 敏感参数概念 ,从而定义了 p 综合距离与 ( p θ)相对激活度 .将关于区间值模糊...给出了FMP的三I解的一般形式 ,证明了关于区间值模糊推理的单调性定理、下确界定理以及存在性定理 .在分析了规则后件相对于前件的敏感性的基础上提出了 p 敏感参数概念 ,从而定义了 p 综合距离与 ( p θ)相对激活度 .将关于区间值模糊推理的FOOL方法细致化为 ( p θ)算法 。展开更多
基金Supported by National Natural Science Foundation of China(61273126)Research Foundation for the Doctoral Program of Higher Education of China(20130172110027)+1 种基金Fundamental Research Funds for the Central Universities(2013ZZ0056,2015ZM073)Ph.D Start-up Fund of Natural Science Foundation of Guangdong Province(2014A030310388)
基金Supported by Youth Foundation of Ningxia Teachers University(QN2010002)Natural Science Foundation of Ningxia(NZ09204)the Program for Innovative Research Team in Ningxia Teachers University(zy201207)
基金Supported by Natural Science Foundation of Heilongjiang Province(A200602)the Science Research Foundation(HITC200710)the Natural Scientific Research Innovation Foundation(HIT.NSRIF.2009053)
基金Supported by the National Natural Science Foundation of China(11526101)the National Natural Science Foundation of China(11461028)+1 种基金the Natural Science Foundation of Jiangxi Province(20151BAB211016)the National Social Science Foundation of China(14CJY053)
基金Ying Hu’s research is supported by the Lebesgue Center of Mathematics“Investissements d’avenir”Program(Grant No.ANR-11-LABX-0020-01),by ANR CAESARS(Grant No.ANR-15-CE05-0024)by ANR MFG(Grant No.ANR-16-CE40-0015-01)+2 种基金Falei Wang’s research is supported by the Natural Science Foundation of Shandong Province for Excellent Youth Scholars(Grant No.ZR2021YQ01)the National Natural Science Foundation of China(Grant Nos.12171280,12031009 and 11871458)the Young Scholars Program of Shandong University.
文摘In this paper,we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in the second unknown z.Using a linearization technique and the BMO martingale theory,we first apply a fixed-point argument to establish the uniqueness and existence result for the case with bounded terminal condition and obstacle.Then,with the help of theθ-method,we develop a successive approximation procedure to remove the boundedness condition on the terminal condition and obstacle when the generator is concave(or convex)with respect to the second unknown.
