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In this paper, the Harnack inequalities and super-Poincar\'{e} inequality forgeneralized CIR model are obtained. Since the noise is degenerate, theintrinsic metric has been introduced to construct the coupling by change ofmeasure. By using isopermetric constant, the optimal estimate of the ratefunction in the super Poincar\'{e} inequality for the associated Dirichlet formis also obtained.

Harnack and Super Poincar\'{e} Inequalities for Generalized Cox-Ingersoll-Ross Model