Jordan decomposition and geometric multiplicity for a class of non-symmetric Ornstein-Uhlenbeck operators

Advances in Difference Equations

Jiying Wang¹  Yulei Rao¹  Yong Chen² 

[1] Business School of Central South University, Changsha, P.R. China;Hunan University of Science and Technology, Xiangtan, P.R. China

关键词: Jordan decomposition;    2-dimensional non-symmetric Ornstein-Uhlenbeck operator;    3-dimensional non-symmetric Ornstein-Uhlenbeck operator;   

DOI  :  10.1186/1687-1847-2014-34

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we calculate the Jordan decomposition for a class of non-symmetric Ornstein-Uhlenbeck operators with the drift coefficient matrix, being a Jordan block, and the diffusion coefficient matrix, being the identity multiplying a constant. For the 2-dimensional case, we present all the general eigenfunctions by mathematical induction. For the 3-dimensional case, we divide the calculation of the Jordan decomposition into three steps. The key step is to do the canonical projection onto the homogeneous Hermite polynomials, and then use the theory of systems of linear equations. Finally, we get the geometric multiplicity of the eigenvalue of the Ornstein-Uhlenbeck operator.

【 授权许可】

CC BY