COMPARISON THEOREMS FOR MULTI-DIMENSIONAL GENERAL MEAN-FIELD BDSDES

In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations(BDSDEs),that is,BDSDEs whose coefficients depend not only on the solution processes but also on their law.The first part of the paper is devoted to the comparison theorem for multi-dimensional mean-field BDSDEs with Lipschitz conditions.With the help of the comparison result for the Lipschitz case we prove the existence of a solution for multi-dimensional mean-field BDSDEs with an only continuous drift coefficient of linear growth,and we also extend the comparison theorem to such BDSDEs with a continuous coefficient.     

具有遗传性疾病和性状的遗传位点分析

为便于进行数据分析,首先将数据中的位点信息由原来字母编码方式转换为数值编码的方式,根据位点的编码信息和患病信息,采用Logistic回归的方法,找出某种疾病最有可能的一个或几个致病位点,同时采用显著性检验进一步对建立的模型进行检验,证明了建立结果的合理性。此外,通过主成分分析,从原有的300个主成分中取出了225个主成分尽可能多地反映原来基因变量的信息,再通过主成分Logistic回归分析找出与疾病最有可能相关的一个或几个基因。最后,采用典型相关分析找出与相关性状有关联的基因位点。     

GENERAL COUPLED MEAN-FIELD REFLECTED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs) under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this c...