由分数噪声驱动的一类分数阶随机偏微分方程的光滑密度研究（英文）  

Smooth Density for a Class of Fractional SPDE with Fractional Noise

作　　者：苍玉权[1] 李沁怡 刘俊峰[1] CANG Yuquan;LI Qinyi;LIU Junfeng(Department of Statistics,Nanjing Audit University,Nanjing,211815,China)

机构地区：[1]南京审计大学统计学系,南京211815

出　　处：《应用概率统计》2018年第3期284-296,共13页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National Natural Science Foundation of China(Grant No.11401313);the Natural Science Foundation of Jiangsu Province(Grant No.BK20161579);the China Postdoctoral Science Foundation(Grant Nos.2014M560368;2015T80475);2014 Qing Lan Project,Financial Engineering Key Laboratory of Jiangsu Province(Grant No.NSK201504);PAPD

摘　　要：本文中,我们研究了由分数噪声驱动的一类分数阶随机偏微分方程,利用Malliavin分析技巧,证明了该类方程的适度解在任意固定的点(t,x)∈[0,T]×R具有光滑密度.In this paper we consider a class of fractional stochastic partial differential equation driven by fractional noise.We prove that the solution admits a smooth density at any fixed point(t,x)∈[0,T]×R with T>0 by using the techniques of Malliavin calculus.

关 键 词：分数阶随机偏微分方程 变系数的稳定类过程生成元 分数噪声 Malliavin分析 光滑密度 

分 类 号：O211.6[理学—概率论与数理统计]