分数Levy过程的随机积分及其驱动的随机微分方程  

Stochastic Integration for Fractional Levy Processes and Stochastic Differential Equations Driven by Fractional Levy Noises

作　　者：吕学斌[1,2] 戴万阳[2] 

机构地区：[1]南京工业大学理学院应用数学系,南京210009 [2]南京大学数学系,南京210093

出　　处：《数学物理学报（A辑）》2013年第6期1022-1034,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(10971249,11001051,10971076,41101509);教育部人文社科规划项目(11YJA910001)资助

摘　　要：基于文献[1]对平方可积纯跳的Levy过程的白噪声分析,把由平方可积纯跳的Levy过程定义的分数Levy过程看作是Levy过程轨道的泛函,将其S-变换意义下的形式导数定义为分数Levy噪声,从而,定义了分数Levy过程的Skorohod积分.进一步地,提出了一类由分数Levy噪声驱动的Volterra方程并研究了其解的存在唯一性,同时提出了一类由分数Levy噪声驱动的随机微分方程并在线性增长条件及Lipschtz条件下证明其解的存在唯一性.In this paper, based on the white noise analysis of square integrable pure-jump Levy process given by [1], we define the formal derivative of fractional Levy process defined by the square integrable pure-jump Levy process as the fractional Levy noises by considering fractional Levy process as the generalized functional of Levy process, and then we define the Skorohod integral with respect to the fractional Levy process. Moreover, we propose a class of stochastic Volterra equations driven by fractional Levy noises and investigate the existence and uniqueness of their solutions; In addition, we propose a class of stochastic differential equations driven by fractional Levy noises and prove that under the Lipschtz and linear conditions there exists unique stochastic distribution-valued solution.

关 键 词：白噪声分析 分数Lévy过程 Skorohod积分 随机微分方程 

分 类 号：O211.6[理学—概率论与数理统计]