# On the Jordan decomposition for a class of non-symmetric Ornstein-Uhlenbeck operators

@article{Chen2012OnTJ, title={On the Jordan decomposition for a class of non-symmetric Ornstein-Uhlenbeck operators}, author={Yong Chen and Yingde Li}, journal={arXiv: Probability}, year={2012} }

In this paper, we calculate the Jordan decomposition (or say, the Jordan canonical form) for a class of non-symmetric Ornstein-Uhlenbeck operators with the drift coefficient matrix being a Jordan block and the diffusion coefficient matrix being identity multiplying a constant. For the 2-dimensional case, we present all the general eigenfunctions by the induction. For the 3-dimensional case, we divide the calculating of the Jordan decomposition into several steps (the key step is to do the…

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