推广线性二阶抛物型方程Cauchy问题解的Feynman-Kac定理

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中更为符合实际，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过程听两个基本性质，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－扩散随机过程的矩不等式，并由此建立了推广的二

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

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.