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Performances of differential absorption ozone lidars with ultraviolet Raman lasers are evaluated by a numerical simulation taking into account the solar-blind effect of stratospheric ozone for daytime observation; they are compared with observations. Calculations predict an ozone density profile up to 5 km in altitude determined during daylight using first and second Stokes lines of H_2, and up to 30 km at night using second Stokes line of CH_4 or D_2, and second and third Stokes lines of H_2 pumped by a KrF laser. A preliminary experiment of the daytime observations and a nighttime result are briefly reported.