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.
