An exponential continuous time GARCH process

In this paper we introduce an exponential continuous time GARCH(p,q) process. It is defined in such a way that it is a continuous time extension of the discrete time EGARCH(p,q) process. We investigate stationarity and moment properties of the new model. An instantaneous leverage effect can be shown for the exponential continuous time GARCH(p,p) model

Late-time acceleration with steep exponential potentials

In this letter, we study the cosmological dynamics of steeper potential than exponential. Our analysis shows that a simple extension of an exponential potential allows to capture late-time cosmic acceleration and retain the tracker behavior. We also perform statefinder and $Om$ diagnostics to distinguish dark energy models among themselves and with $\Lambda$CDM. In addition, to put the observational constraints on the model parameters, we modify the publicly available CosmoMC code and use an integrated data base of baryon acoustic oscillation, latest Type Ia supernova from Joint Light Curves sample and the local Hubble constant value measured by the Hubble Space Telescope.Comment: 9 pages, 5 figures, 2 table