The ballast is typically an electronic unit which uses a high frequency SMPS design to minimize its size and improve efficiency. I believe the voltage and current waveform is a chopped rectified sine-wave at the mains frequency. A Google of electronic ballast gives additional info.
Simple electronic ballast used for small wattage bulbs and CFL are typically full wave rectified AC mains with some amount of filtering to reduce ripple to about 30 to 50 vdc from the 170 vdc peak.
The DC supply is then chopped at 25 kHz to 40 kHz. At this point it is same scheme as 60 Hz except bulb is more efficient when excited by higher freq so slightly higher XL at chopped frequency is used. Run current will be slightly less. At high frequency the coil is small ferrite core inductor with proper XL at chop frequency. Bimetalic starter is too slow for high frequency chop so a small capacitor is used.
For maximum bulb life it is important to have 50% duty cycle on applied AC to get equal current flow back and forth through bulb. When AC is not 50% the available mercury will migrate to one end resulting in a faster plate out of mercury to surface of glass on one end. Evenually there will not be enough mercury to vaporize and bulb will not strike up.