Constraints on $\Lambda(t)$CDM models as holographic and agegraphic dark energy with the observational Hubble parameter data

The newly released observational $H(z)$ data (OHD) is used to constrain $\Lambda(t)$CDM models as holographic and agegraphic dark energy. By the use of the length scale and time scale as the IR cut-off including Hubble horizon (HH), future event horizon (FEH), age of the universe (AU), and conformal time (CT), we achieve four different $\Lambda(t)$CDM models which can describe the present cosmological acceleration respectively. In order to get a comparison between such $\Lambda(t)$CDM models and standard $\Lambda$CDM model, we use the information criteria (IC), $Om(z)$ diagnostic, and statefinder diagnostic to measure the deviations. Furthermore, by simulating a larger Hubble parameter data sample in the redshift range of $0.1<z<2.0$, we get the improved constraints and more sufficient comparison. We show that OHD is not only able to play almost the same role in constraining cosmological parameters as SNe Ia does but also provides the effective measurement of the deviation of the DE models from standard $\Lambda$CDM model. In the holographic and agegraphic scenarios, the results indicate that the FEH is more preferable than HH scenario. However, both two time scenarios show better approximations to $\Lambda$CDM model than the length scenarios.