推广线性二阶抛物型方程Cauchy问题解的Feynman-Kac定理  

Feynman-Kac Theorem about Cauchy Problem of Extended Second-Order Parabolic Equation

作　　者：林建忠[1] 叶中行[1] 

机构地区：[1]上海交通大学应用数学系,上海200030

出　　处：《上海交通大学学报》2000年第4期582-588,共7页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金重大项目"金融数学;金融工程;金融管理"!( 79790 13 0 )

摘　　要：在金融数学中 ,用跳跃 -扩散型随机微分方程模型描述证券价格过程更为符合实际 ,讨论了由高维 Poisson过程和 Brown运动共同驱动的随机微分方程的 Feynman- Kac定理 .首先建立了高维 Poisson过程的两个基本性质 ,在此基础上 ,导出了推广的向后热传导方程 Cauchy问题解的Feynman- Kac定理 .其次 ,利用 Burkholder不等式建立了跳跃 -扩散型随机过程的矩不等式 ,并由此建立了推广的二阶线性抛物型方程 Cauchy问题解的 Feynman-In finacial mathematics, the security price processes model described by jump diffusion stochastic differential equation is advantageous from an applied point of view. This paper developed Feynman Kac theorem in connection with multidimensional Poisson jump diffusion stochastic differential equation. First, it derived two properties about several dimensional Poisson processes. Based on these relations, it provided a representation for the solution of extended backward heat conduction equation subjected to certain terminal condition. Then it obtained the moment inequality of jump diffusion stochastic processes by use of Burkholder inequality. Moreover, the Feynman Kac formula associated with the exteded second order linear parabolic equation was established.

关 键 词：随机微分方程 抛物型方程 柯西问题 F-K定理 

分 类 号：O175.26[理学—数学] O211.63[理学—基础数学]